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

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 and b = π/3

Answer 2

Answer:

Pie/3

Explanation: