Question

If a vector and b vector are two non-zero vectors such that |a+b|=|a-b|/2 and a=2b then the angle between a vector and b vector is?????

Answer 1

Given, a+b = a-b/2

On squaring both sides we get

(a+b)^2 = (a-b)^2/4

a^2 + b^2 + 2ab = a^2 + b^2 - 2ab/4

4a^2 + 4b^2 + 8ab - a^2 - b^2 + 2ab

3a^2 + 3b^2 + 10ab.

Given that a = 2b.

3(2b)^2 + 3b^2 + 10 * (2b) * b cos theta = 0

3 * 4b^2 + 3b^2 + 20b^2 cos theta = 0

12b^2 + 3b^2 + 20b^2 cos theta = 0

15b^2 + 20b^2 cos theta = 0

cos theta = -15/20

       theta = cos^-1 (-3/4).

Answer 2

Answer:

Step-by-step explanation:

Given, a+b = a-b/2

On squaring both sides we get

(a+b)^2 = (a-b)^2/4

a^2 + b^2 + 2ab = a^2 + b^2 - 2ab/4

4a^2 + 4b^2 + 8ab - a^2 - b^2 + 2ab

3a^2 + 3b^2 + 10ab.

Given that a = 2b.

3(2b)^2 + 3b^2 + 10 * (2b) * b cos theta = 0

3 * 4b^2 + 3b^2 + 20b^2 cos theta = 0

12b^2 + 3b^2 + 20b^2 cos theta = 0

15b^2 + 20b^2 cos theta = 0

cos theta = -15/20

      theta = cos^-1 (-3/4)