The acute angle between the two lines whose direction ratios are

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 QuestionsMultiple Choice Questions

381.

The distance between the lines x - 13 = y + 2- 2 = z - 12 and the plane 2x + 2y - z = 6 is

  • 9

  • 3

  • 2

  • 1


382.

The cosine of the angle between any two diagonals of a cube is

  • 13

  • 23

  • - 23

  • 12


383.

ABCD is a parallelogram, with AC, BD as diagonals, then AC - BD is equal to

  • 4AB

  • AB

  • 3AB

  • 2AB


384.

If θ is the angle between a and b and a × b = a . b, then θ is equal to

  • 0

  • π

  • π2

  • π4


Advertisement
385.

a, b, c, d are coplanar vectors, then (a x b) x (c x d) is equal to

  • 0

  • 1

  • a

  • b


386.

If the foot of the perpendicular from (0, 0, 0) to the plane is (1, 2, 2), then the equation ofthe plane is

  • - x + 2y + 8z - 9 = 0

  • x + 2y + 2z - 9 = 0

  • x + y + z - 5 = 0

  • x + 2y - 3z + 1 = 0


387.

If P = (0, 1, 2), Q =(4, - 2, 1), O =(0, 0, 0), then POQ is equal to

  • π2

  • π4

  • π6

  • π3


388.

A variable plane is at a constant distance h from the origin and meets the coordinate axes in A, B, C. Locus of centroid of ABC is

  • x2 + y2 + z2 = h- 2

  • x2 + y2 + z2 = 4h- 2

  • x2 + y2 + z2 = 16h2

  • 1x2 + 1y2 + 1z2 = 9h2


Advertisement
Advertisement

389.

The acute angle between the two lines whose direction ratios are given by l + m - n = 0 and  l2 + m2 + n2 = 0, is

  • 0

  • π6

  • π4

  • π3


D.

π3

Given that               l + m + n = 0   ...iand   l2 + m2 + n2 = 0From equation i l = -m - nPutting in equation ii we get m - n2 + m2 - n2 = 0 m2 + n2  - 2mn + m2 - n2 = 0 2m2 - 2mn = 0 m = 0, m = nFrom equation (i), if m = 0, thenl = m  l : m : n = 1 : 0 : 1If m = n, then l = 0  l : m : n = 0 : 1 : 1If θ is the acute angle, thencosθ = 1 . 0 + 0 . 1 + 1 . 11 + 11 + 1          = 12 = cosπ3  θ = π3


Advertisement
390.

The direction ratios of normal to the plane passing through (0, 0, 1), (0, 1, 2) and (1, 0, 3) are

  • (2, 1, - 1)

  • (1, 0, 1)

  • (0, 0, - 1)

  • (1, 0, 0)


Advertisement