If a, b, c are non-coplanar unit vectors such thata ×&

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 Multiple Choice QuestionsMultiple Choice Questions

41.

If the four points with position vectors - 2i^ + j^ + k^, i^ + j^ + k^, j^ - k^ and λj^ + k^ are coplanar, then λ is equal to

  • 1

  • 2

  • - 1

  • 0


42.

The equation zz + az + az + b = 0, represents a circle, if

  • a2 = b

  • a2 > b

  • a2 <b

  •  None of the above


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43.

If a, b, c are non-coplanar unit vectors such that

a × b × c = b + c2, then the angle between a and b is

  • 3π4

  • π4

  • π2

  • π


A.

3π4

We have,

a × b × c = b +c2 a . cb - a . bc = 12b + 12c a . c - 12b - a . b + 12c = 0 0a + a . c - 12b + - a . b - 12c = 0 a . c - 12 = 0 and - a . b - 12 = 0             a, b, c are non-coplanar

Now,          a . b = - 12 abcosθ = - 12           cosθ = - 12          a, b, c are unit vectors                   θ = 3π4


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44.

If a, b, c and a', b',c' form a reciprocal system of vectors, then a . a'+ b . b' + c · c' is equal to

  • 0

  • 1

  • 2

  • 3


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45.

If a, b, c are three non - zero vectors which are pairwise non-collinear. Also, a + 3b is collinear with c and b + 2c is collinear with a, then a + 3b + 6c is

  • c

  • 0

  • a + c

  • a


46.

If d = a x b + b x c + c x a is a non-zero vector and (d · c) (a x b) + (d · a) (b x c) + (d . b) (c x a) = 0, then

  • a + b + c = d

  • a = b = c

  • a, b and c are coplanar

  • None of the above


47.

Let u, v and w be such that u = 1, v = 2 and w = 3. If the projection of v along u is equal to that of w along u and vectors v and w are perpendicular to each other, then u - v + w equals

  • 2

  • 7

  • 14

  • 14


48.

If a and b are two vectors, such that a . b < 0 and a . b = a × b then the angle between vectors a and b is

  • 3π4

  • π4

  • π

  • 7π4


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49.

A tetrahedron has vertices at 0(0, 0, 0), A(1, - 2, 1), B (-2, 1, 1) and C (1, - 1, 2). Then, the angle between the faces OAB and ABC will be

  • cos-112

  • cos-1- 16

  • cos-1- 13

  • cos-114


50.

If a, b and c are three non-coplanar vectors, then (a + b - c) . [(a - b) x (b - c)] equals

  • 0

  • a . b × c

  • a . c × b

  • 3a . b × c


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