The scalar product of the vector  with a unit vector along the

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

311.

Find the angle between the vector straight i with hat on top minus straight j with hat on top space and space straight j with hat on top space minus space straight k with hat on top.

960 Views

312.

Find the value of 'p' for which the vectors 3 straight i with hat on top plus 2 straight j with hat on top plus 9 straight k with hat on top space and space straight i with hat on top minus 2 straight p straight j with hat on top plus 3 straight k with hat on top are parallel.

184 Views

313.

If the cartesian equations of a line are fraction numerator 3 minus straight x over denominator 5 end fraction equals fraction numerator straight y plus 4 over denominator 7 end fraction equals fraction numerator 2 straight z minus 6 over denominator 4 end fraction comma write the vector equation for the line. 

140 Views

314. If space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space perpendicular space vectors comma space open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar space equals space 13 space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 5 space and space find space the space value space of space open vertical bar straight b with rightwards arrow on top close vertical bar.
135 Views

Advertisement
315.

Show that the four points A, B, C and D with position vectors
4 straight i with hat on top plus 5 straight j with hat on top plus straight k with hat on top comma negative straight j with hat on top minus straight k with hat on top comma space 3 straight i with hat on top plus 9 straight j with hat on top plus 4 straight k with hat on top space and space 4 left parenthesis negative straight i with hat on top plus straight j with hat on top plus straight k with hat on top right parenthesis respectively are coplanar.

373 Views

Advertisement

316.

The scalar product of the vector straight a with rightwards arrow on top equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top with a unit vector along the sum of vectors straight b with rightwards arrow on top equals 2 straight i with hat on top plus 4 straight j with hat on top minus 5 straight k with hat on top space space and space straight c with rightwards arrow on top space equals space straight lambda straight i with hat on top plus 2 straight j with hat on top plus 3 straight k with hat on top is equal to one. Find the value of straight lambda and hence find the unit vector along straight b with rightwards arrow on top plus straight c with rightwards arrow on top.


Given that
straight b with rightwards arrow on top space equals space 2 straight i with hat on top plus 4 straight j minus 5 straight k
straight c with rightwards arrow on top equals straight lambda straight i with hat on top plus 2 straight j plus 3 straight k
Now consider the sum of vectors straight b with rightwards arrow on top plus straight c with rightwards arrow on top colon
straight b with rightwards arrow on top plus straight c with rightwards arrow on top equals space open parentheses 2 straight i with hat on top plus 4 straight j minus 5 straight k close parentheses plus open parentheses straight lambda straight i with hat on top plus 2 straight j plus 3 straight k close parentheses
space space rightwards double arrow space space straight b with rightwards arrow on top plus straight c with rightwards arrow on top space equals space left parenthesis 2 plus straight lambda right parenthesis straight i with hat on top plus 6 straight j minus 2 straight k
Let space straight n with hat on top space be space the space unit space vector space along space the space sum space of space vectors space straight b with rightwards arrow on top plus straight c with rightwards arrow on top colon
straight n with hat on top space equals fraction numerator left parenthesis 2 plus straight lambda right parenthesis straight i with hat on top plus 6 straight j minus 2 straight k over denominator square root of left parenthesis 2 plus straight lambda right parenthesis squared plus 6 squared plus 2 squared end root end fraction
The space scalar space product space of space straight a with rightwards arrow on top space and space straight n space is space 1. space Thus comma space
straight a with rightwards arrow on top. straight n with hat on top space equals open parentheses straight i with hat on top plus straight j plus straight k close parentheses. space open parentheses fraction numerator left parenthesis 2 plus straight lambda right parenthesis straight i with hat on top plus 6 straight j minus 2 straight k over denominator square root of left parenthesis 2 plus straight lambda right parenthesis squared plus 6 squared plus 2 squared end root end fraction close parentheses
rightwards double arrow 1 space equals fraction numerator 1 left parenthesis 2 plus straight lambda right parenthesis plus 1.6 minus 1.2 over denominator square root of left parenthesis 2 plus straight lambda right parenthesis squared plus 6 squared plus 2 squared end root end fraction
rightwards double arrow square root of left parenthesis 2 plus straight lambda right parenthesis squared plus 6 squared plus 2 squared end root space equals space 2 plus straight lambda plus 6 minus 2
rightwards double arrow square root of left parenthesis 2 plus straight lambda right parenthesis squared plus 6 squared plus 2 squared end root space equals straight lambda plus 6
rightwards double arrow left parenthesis 2 plus straight lambda right parenthesis squared plus 40 space equals space left parenthesis straight lambda plus 6 right parenthesis squared
rightwards double arrow straight lambda squared plus 4 straight lambda plus 4 plus 40 equals straight lambda squared plus 12 straight lambda plus 36
rightwards double arrow 4 straight lambda plus 44 equals 12 straight lambda plus 36
rightwards double arrow 8 straight lambda equals 8
rightwards double arrow straight lambda equals 1
Thus, n is:
straight n equals fraction numerator left parenthesis 2 plus 1 right parenthesis straight i with hat on top plus 6 straight j minus 2 straight k over denominator square root of left parenthesis 2 plus 1 right parenthesis squared plus 6 squared plus 2 squared end root end fraction
rightwards double arrow space straight n space equals space fraction numerator 3 straight i with hat on top plus 6 straight j minus 2 straight k over denominator square root of 3 squared plus 6 squared plus 2 squared end root end fraction
rightwards double arrow straight n space equals fraction numerator 3 straight i with hat on top plus 6 straight j minus 2 straight k over denominator square root of 49 end fraction
rightwards double arrow straight n space equals space fraction numerator 3 straight i with hat on top plus 6 straight j minus 2 straight k over denominator 7 end fraction
rightwards double arrow straight n space equals 3 over 7 straight i with hat on top plus 6 over 7 straight j minus 2 over 7 straight k



336 Views

Advertisement

 Multiple Choice QuestionsLong Answer Type

317.

Find the distance of the point (2, 12, 5) from the point of intersection of the line 
straight r with rightwards arrow on top equals 2 straight i with hat on top minus 4 straight j with hat on top plus 2 straight k with hat on top plus straight lambda open parentheses 3 straight i with hat on top plus 4 straight j with hat on top plus 2 straight k with hat on top close parentheses space and space the space plane space straight r with rightwards arrow on top. open parentheses straight i with hat on top minus 2 straight j with hat on top plus straight k with hat on top close parentheses equals 0.

140 Views

 Multiple Choice QuestionsShort Answer Type

318.

If a unit vector straight a with rightwards arrow on top space equals space straight x straight i with hat on top plus 2 straight j with hat on top minus straight z straight k with hat on top and straight b with rightwards arrow on top space equals space 3 straight i with hat on top minus straight y straight j with hat on top plus straight k with hat on top are two equal vectors, then write the value of x+y+z.

161 Views

Advertisement
319.

If a unit vector straight a with rightwards arrow on top makes angle straight pi over 3 space with space straight i with hat on top comma space space space straight pi over 4 space with space straight j with hat on top space and space acute space angle space straight theta space with space straight k with hat on top comma space then find the value of straight theta.

151 Views

320.

If straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two vectors such that open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar equals open vertical bar straight a with rightwards arrow on top close vertical bar comma then prove that vector 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top is perpendicular to vector straight b with rightwards arrow on top.

158 Views

Advertisement