﻿ If the vectors  are mutually orthogonal, then (λ,μ) is equal

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## Vector Algebra

#### Multiple Choice Questions

1.

The Boolean Expression (p∧~q)∨q∨(~p∧q) is equivalent to:

• ~p ∧ q

• p ∧ q

• p ∨ q

• p ∨ q

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2.

Let, a, b and c be three non-zero vectors such that no two of them are collinear and  if θ is the angle between vectors b and  c, then a value of sin θ is

220 Views

3.

If the vectors AB = 3î + 4k̂ and AC = 5î - 2ĵ + 4k̂ are the sides of a Δ ABC, then the length of the median through A is

• √18

• √72

• √33

• √45

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4.

Let  be  two unit vectors. If the vectors  and  are perpendicular to each other, then the angle between  is

• π/6

• π/2

• π/3

• π/3

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5.

Let ABCD be a parallelogram such that  and ∠BAD be an acute angle. If   is the vector that coincides with the altitude directed from the vertex B the side AD, then  is given byLet ABCD be a parallelogram such that AB = q,AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by (1)

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6.
• -5

• -3

• 5

• 5

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7.

The vector  are not perpendicular  and  are two vectors satisfying:  The vector  is equal to

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8.

The circle x2+ y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

• -85 < m < -35

• -35 < m < 15

• 15 < m < 65

• 15 < m < 65

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9.

Let  and . Then, the vector b satisfying a x b + c = 0  and a.b  = 3

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# 10.If the vectors  are mutually orthogonal, then (λ,μ) is equal to (-3,2) (2,-3) (-2,3) (-2,3)

A.

(-3,2)

since, the given vectors mutually orthogonal, therefore
a.b = 2-4+2 = 0
a.c = λ-1 + 2μ = 0   ....(i)
b.c = 2λ + 4 +μ = 0  ... (ii)
On solving Eqs. (i) and (ii), we get
μ  = 2 and λ = - 3
Hence, (λ,μ) = (-3,2)

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