Question

Two vectors lie with their tails at the same point. When the angle between
them is increased by 20° their scalar product has the same magnitude but
changes from positive to negative. The original angle between them was:
A.O
B. 60°
C.70°
D. 80°
​

Answer 1

Explanation:

Pic attached

Answer 2

Given info : Two vectors lie with their tails at the same point. When the angle between them is increased by 20° their scalar product has the same magnitude but changes from positive to negative.

To find : The original angle between them was ...

solution : let initial angle between the vectors (let A and B) is θ.

scalar product , R = |A| |B| cosθ

now angle is increased by 20°,

scalar product , R = |A| |B| cos(θ + 20°)

a/c to question,

if angle between them is increased by 20° , their scale product has the same magnitude but changes from positive to negative.

i.e., -|A| |B| cosθ = |A| |B| cos(θ + 20°)

⇒-cosθ = cos(θ + 20°)

⇒cos(180° - θ) = cos(θ + 20°)

⇒180° - θ = θ + 20°

⇒θ = 80°

Therefore the original angle between them was 80°