﻿ If  are non–coplanar vectors and p, q are real numbers, then

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11.
• 1/8

• 25/8

• 2

• 2

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# 12.If  are non–coplanar vectors and p, q are real numbers, then the equality  holds for exactly one value of (p, q) exactly two values of (p, q) more than two but not all values of (p, q) more than two but not all values of (p, q)

A.

exactly one value of (p, q)

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13.

If , then the maximum value of |Z| is equal to

• 2

• 2

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14.

The vector  lies in the plane of the vectors  and bisects the angle between .Then which one of the following gives possible values of α and β?

• α = 2, β = 2

• α = 1, β = 2

• α = 2, β = 1

• α = 2, β = 1

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15.

The non−zero verctors are related by .Then the angle between  is

• 0

• π/4

• π/2

• π/2

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16.

If are unit vectors and θ is the acute angle between them, then  is a unit vector for

• Exactly two values of θ

• More than two values of θ

• No value of θ

• No value of θ

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17.

A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. The angle of projection is-

• 45°

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18.
• 0

• -1

• -2

• -2

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19.

ABC is a triangle, right angled at A. The resultant of the forces acting along  respectively is the force along  where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

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20.  are any three vectors such that
• inclined at an angle of π/3 between them

• inclined at an angle of π/6 between them

• perpendicular

• perpendicular

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