Question

Two equal vectors are along adjacent sides of a parallelogram and one of the diagonals is√3 times the other. the angle between the vectors is.
a) π/3 b) π/6 c) 2π/3 d)π/4​

Answer 1

Answer:

Given:

Two vectors a and b are along the adjacent sides of a parallelogram.

║a║=║b║

The length of one of the diagonal is √3 times the length of the other diagonal.

To find:

The angle between the two vectors a and b.

Solution:

Let the angle between the two vectors a and be α

The two diagonal vectors of the parallelogram can be given by (a+b) and (a-b).

║a+b║² = ║a║²+║b║²+2║a║║b║cosα = 2║a║²(1+cosα)

║a-b║² = ║a║²+║b║²-2║a║║b║cosα = 2║a║²(1-cosα)

It is given that, ║a+b║ = √3 ║a-b║

⇒║a+b║² = 3║a-b║²

⇒2║a║²(1+cosα) = 6║a║²(1-cosα)

⇒1 + cosα = 3 - 3cosα

⇒4cosα = 2

⇒cosα = 1/2

⇒α = π/3

Answer:

The angle between the two vectors a = π/3