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.

Three Dimensional Geometry

Short Answer Type

251. Find the angle between the line

fraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator straight y minus 2 over denominator negative 1 end fraction space equals space fraction numerator straight z plus 1 over denominator 1 end fraction

and the plane 2x – y + z= 1.

83 Views

252.

Find the angle between the line $fraction numerator straight x plus 1 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 4 end fraction$ and the plane 2x + y – 3z + 4 = 0.

97 Views

253. Find the angle between the lines

fraction numerator straight x plus 1 over denominator 2 end fraction space equals space straight y over 3 space equals space fraction numerator straight z minus 3 over denominator 6 end fraction

and the plane 10x + 2y – 11z = 3.

96 Views

254. Find the angle between the line

fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 1 end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction

and the plane 3x + 4y + z + 5 = 0.

91 Views

255.
Find the angle between the line $straight r with rightwards arrow on top space equals space open parentheses straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top close parentheses space plus space straight lambda space open parentheses 2 straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top close parentheses$ and the plane $straight r with rightwards arrow on top. space open parentheses 2 straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 4$

The equation of line is $straight r with rightwards arrow on top space equals space open parentheses straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top close parentheses space plus space straight lambda space open parentheses 2 straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top close parentheses$
$therefore space space space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus 3 space straight k with hat on top$
The equation of plane is $straight r with rightwards arrow on top. space open parentheses 2 straight i with hat on top plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 4$
$therefore space space space space space straight n with rightwards arrow on top space equals space space 2 straight i with hat on top plus straight j with hat on top space minus space straight k with hat on top$
Let θ be the angle between the line and plane $therefore space space sin space straight theta space equals space fraction numerator straight b with rightwards arrow on top. space straight n with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar space open vertical bar straight n with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 2 right parenthesis space plus space left parenthesis negative 1 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis 3 right parenthesis thin space left parenthesis negative 1 right parenthesis over denominator square root of 4 plus 1 plus 9 end root space square root of 4 plus 1 plus 1 end root end fraction space equals space fraction numerator 0 over denominator square root of 4 space square root of 6 end fraction space equals space 0$