12 maths unit 6 EM

If a̅ and b̅ are parallel vector, then [a̅,c̅,b̅] is equal to

• 2

• -1

• 1

• o

If a vector α̅ lies in the plane of β̅ and γ̅, then

• [α̅, β̅, γ̅ ] =1

• [α̅, β̅, γ̅ ] = -1

• [α̅, β̅, γ̅ ] = 0

• [α̅, β̅, γ̅ ] = 2

If a̅.b̅ = b̅.c̅ = c̅.a̅ = 0, then the value of [a̅, b̅, c̅] is

• |a̅| |b̅| |c̅|

• 1/3 |a̅| |b̅| |c̅|

• 1

• -1

If a̅, b̅, c̅ are three unit vector such that a̅ is perpendicular to b̅, and is parallel to c̅ then a̅ₓ(b̅ₓc̅) is equal to

• a̅

• b̅

• c̅

• 0̅

If [a̅, b̅, c̅] = , then the value of a̅.(b̅ₓc̅)/(c̅ₓa̅).b̅ + b̅.(c̅ₓa̅)/(a̅ₓb̅).c̅ + c̅.(a̅ₓb̅)/(c̅ₓb̅).a̅ is

• 1

• -1

• 2

• 3

The volume of the parallelepiped with its edges represented by the vectors i^ +j^, i^+2j^, i^+j^+πk^ is

• π/2

• π/3

• π

• π/4

If a̅ and b̅ are unit vector such that [a̅, b̅, a̅xb̅]= 1/4, then the angle between a̅ and b̅ is

• π/6

• π/4

• π/3

• π/2

If a̅ = i^+j^+k^, b̅ = i^+j^, c̅ = i^ and (a̅xb̅)xc̅ = λa̅ + μb̅, then the value of λ+μ is

• 0

• 1

• 2

• 3

If a̅, b̅, c̅ are three non-coplanar unit vector such that a̅x(b̅xc̅) = b̅+c̅/√2, then the angle between a̅ and b̅ is

• π/2

• 3π/2

• π/4

• π

If a̅, b̅, c̅are non coplanar, non zero vector such that [a̅, b̅, c̅] = 3,then {[a̅xb̅, b̅xc̅, c̅xa̅]}² is equal to

• 81

• 9

• 27

• 18