Question

Find the magnitude of two vectors , having the same magnitude and such that the angle between them is 60° and their scalar product is .

Answer 1

The given vectors a → and b → have same magnitude, that is, | a → |=| b → |, θ= 60 0 and a → ⋅ b → = 1 2 .

Formula used for dot product is,

a → ⋅ b → =| a → || b → |cosθ

Here, the angle between a → and b → is θ.

Substitute the values in the above formula.

1 2 =| a → || a → |×cos 60 0 1 2 = | a → | 2 × 1 2 | a → | 2 =1 | a → |=±1

The magnitude of vector is always positive so,

| a → |=1

Thus, the magnitude of vector a → and b → is 1.