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

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 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


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385.

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

  • 0

  • 1

  • a

  • b


A.

0

We have, a, b, c and d are coplanar vectors, then a × b and c × d are perpendicular on the same plane, therefore, a x b and c x d both are parallel to each other, then a × b × c × d = 0


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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


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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


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)


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