Find the equation of the plane containing the lines:       

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 QuestionsLong Answer Type

281. Find the vector and cartesian equation of the plane containing the two lines
                straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space plus space 5 space straight k with hat on top right parenthesis
and    straight r with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space space 3 space straight j with hat on top space minus space 7 space straight k with hat on top space plus space straight mu space left parenthesis 3 straight i with hat on top space minus space 2 space straight j with hat on top space plus space space 5 space straight k with hat on top right parenthesis

72 Views

 Multiple Choice QuestionsShort Answer Type

Advertisement

282. Find the equation of the plane containing the lines:
         fraction numerator straight x minus 4 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 4 end fraction space equals space fraction numerator straight z minus 2 over denominator 5 end fraction
and    fraction numerator straight x minus 3 over denominator 1 end fraction space equals space fraction numerator straight y minus 2 over denominator negative 4 end fraction space equals space straight z over 5


The equations of lines are
           fraction numerator straight x minus 4 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 4 end fraction space equals space fraction numerator straight z minus 2 over denominator 5 end fraction
and       fraction numerator straight x minus 3 over denominator 1 end fraction space equals fraction numerator straight y minus 2 over denominator negative 4 end fraction space equals space straight z over 5
The equation of plane containing these two lines is
                      open vertical bar table row cell straight x minus 4 end cell cell straight y minus 3 end cell cell straight z minus 2 end cell row 1 4 5 row 1 cell negative 4 end cell 5 end table close vertical bar space equals space 0
or    left parenthesis straight x minus 4 right parenthesis thin space open vertical bar table row 4 5 row cell negative 4 end cell 5 end table close vertical bar space minus space left parenthesis straight y minus 3 right parenthesis space open vertical bar table row 1 5 row 1 5 end table close vertical bar space plus space left parenthesis straight z minus 2 right parenthesis space open vertical bar table row 1 4 row 1 cell negative 4 end cell end table close vertical bar space equals space 0
or    (x – 4) (20 + 20) – (y – 3) (5 – 5) + (z – 2) (– 4 – 4) = 0
or    40 (x – 4) – 8 (z – 2) = 0 or 5 (x – 4)–(z – 2) = 0
or    5x – 20-z + 2 = 0
or    5x – z – 18 = 0
82 Views

Advertisement

 Multiple Choice QuestionsLong Answer Type

283. Find the equation of the plane passing through the points (3, 2, 1) and (0, 1, 7) and parallel to the line straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top space plus space straight lambda left parenthesis straight i with hat on top space minus space straight j with hat on top space minus space straight k with hat on top right parenthesis.
74 Views

284. Find the equation of the plane passing through the points (1, 2, 3) and (0. –1, 0) and parallel to the line fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 2 over denominator 3 end fraction space equals space fraction numerator straight z over denominator negative 3 end fraction.
87 Views

Advertisement
285. Find the equation of the plane passing through the points (3, 2, 2) and (1, 0, –1) parallel to the line fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y minus 1 over denominator negative 2 end fraction space equals fraction numerator straight z minus 2 over denominator 3 end fraction.
108 Views

286. Find the equation of the plane passing through the origin and parallel to the vectors straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top space space space and space space 3 space straight i with hat on top space minus space straight k with hat on top.
97 Views

 Multiple Choice QuestionsShort Answer Type

287. Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, –4) and parallel to the lines
             straight r with rightwards arrow on top space equals straight i with hat on top space plus space 2 space straight j with hat on top space minus space 4 space straight k with hat on top space plus space straight lambda open parentheses 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space 6 space straight k with hat on top close parentheses
and       straight r with rightwards arrow on top space equals space straight i with hat on top space minus space 3 space straight j with hat on top space plus space space 5 space straight k with hat on top space plus space straight mu space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses

87 Views

 Multiple Choice QuestionsLong Answer Type

288. Show that the lines:
fraction numerator straight x minus 1 over denominator 2 end fraction space equals fraction numerator straight y minus 2 over denominator 3 end fraction space equals space fraction numerator straight z minus 3 over denominator 4 end fraction space and space fraction numerator straight x minus 4 over denominator 5 end fraction space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals straight z intersect. Find the point of intersection also. 
91 Views

Advertisement
289. Show that the lines fraction numerator straight x plus 3 over denominator negative 3 end fraction space equals space fraction numerator straight y minus 1 over denominator 1 end fraction space equals space fraction numerator straight z minus 5 over denominator 5 end fraction space and space fraction numerator straight x plus 1 over denominator negative 1 end fraction space equals fraction numerator straight y minus 2 over denominator 2 end fraction space equals fraction numerator straight z minus 5 over denominator 5 end fraction are coplanar.
82 Views

290. Show that the lines fraction numerator straight x minus 5 over denominator 4 end fraction space equals space fraction numerator straight y minus 7 over denominator 4 end fraction space equals space fraction numerator straight z plus 3 over denominator negative 5 end fraction and fraction numerator straight x minus 8 over denominator 7 end fraction space equals space fraction numerator straight y minus 4 over denominator 1 end fraction space equals space fraction numerator straight z minus 5 over denominator 3 end fraction intersect each other. 
96 Views

Advertisement