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

241. Find the distance between the point P(6, 5, 9) and the plane determined by the points A(3,–1, 2), B(5, 2,4) and C(–1,–1, 6).

75 Views

242. Find the distance of the point (2, 3, 4) from the plane
$straight r with rightwards arrow on top. space open parentheses 3 space straight i with hat on top space minus space 6 space straight j with hat on top space plus space 2 space straight k with hat on top close parentheses space equals space minus 11.$

The equation of the plane is

straight r with rightwards arrow on top. space left parenthesis 3 space straight i with hat on top space minus space 6 space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis space equals space minus 11

or space space left parenthesis straight x straight i with hat on top space plus space straight y straight j with hat on top space space plus space straight z straight k with hat on top right parenthesis. space space left parenthesis 3 straight i with hat on top space minus space 6 straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis equals space minus 11 or space space 3 straight x minus 6 straight y plus 2 straight z space equals space minus 11 or space space 3 straight x minus 6 straight y plus 2 straight z plus 11 space equals space 0

Let p be the length of perpendicular from (2, 3,4) to the plane.

therefore space space space space straight p space space equals space fraction numerator 3 left parenthesis 2 right parenthesis space minus space 6 left parenthesis 3 right parenthesis space plus space 2 left parenthesis 4 right parenthesis space plus space 11 over denominator square root of left parenthesis 3 right parenthesis squared space plus space left parenthesis negative 6 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end fraction space space space space space space space space space space space space equals space fraction numerator 6 minus 18 plus 8 plus 11 over denominator square root of 9 plus 36 plus 4 end root end fraction space equals space fraction numerator 7 over denominator square root of 49 end fraction space equals space 7 over 7 space equals space 1

79 Views

243. Find the distance of a point (2, 5, -3) from the plane

straight r with rightwards arrow on top. space open parentheses 6 straight i with hat on top space minus space 3 space straight j with hat on top space plus space 2 space straight k with hat on top close parentheses space equals space 4.

93 Views

244. If the product of distances of the point (1,1,1) from the origin and the plane x – y + z + k = 0 be 5, then find the value of k.

86 Views

245. If the points (1, 1, p) and (– 3, 0, 1) be equidistant from the plane

straight r with rightwards arrow on top. space left parenthesis 3 space straight i with hat on top space plus space 4 space straight j with hat on top space minus space 1 space 2 space straight k with hat on top right parenthesis space plus space 13 space equals space 0 comma

then find value of p.

82 Views

246.

Find the angle between the line
$straight r with rightwards arrow on top space equals space left parenthesis 2 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top right parenthesis space plus space straight lambda space left parenthesis 2 space straight i with hat on top space minus space 3 space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis$ and the plane
$straight r with rightwards arrow on top. space left parenthesis 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 5 space straight k with hat on top right parenthesis space equals space 4.$

74 Views

247.

Find the angle between the line $straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space plus 3 space straight j with hat on top space plus space 9 space straight k with hat on top space plus space straight lambda left parenthesis 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space 4 space straight k with hat on top right parenthesis$ and the plane $straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top close parentheses space equals space 5$

76 Views

248.

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

78 Views

249. Find the angle between the line

straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top close parentheses space space plus space straight lambda 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

and the plane

straight r with rightwards arrow on top. space open parentheses 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 close parentheses space equals space 4

73 Views

250.

Find the angle between the line $straight x over 4 space equals space fraction numerator straight y minus 2 over denominator 3 end fraction space equals space fraction numerator straight z minus 1 over denominator 6 end fraction$ and the plane x + 2y + 2 + 3 = 0

90 Views