Question

It `veca + vecb + vecc = 0, |veca| = sqrt37, |vecb| = 3 and |vecc| = 4`, then angle between `vecb and vecc` is ______.

विकल्प

• `pi/6`

• `pi/4`

• `pi/3`

• `pi/2`

Answer 1

It `veca + vecb + vecc = 0, |veca| = sqrt37, |vecb| = 3 and |vecc| = 4`, then angle between `vecb and vecc` is `bbunderline(pi/3)`.

Explanation:

Given: `veca + vecb + vecc = 0`

`vecb + vecc = -veca`

`|vecb + vecc|^2 = |-a|^2`

`|vecb|^2 + |c|^2 + 2 vecb.vecc = |veca|^2`

`|vecb|^2 + |c|^2 + 2|vecb||vecc| cos θ = |veca|^2` 

Given, `|a| = sqrt37, |b| = 3, |c| = 4     ...(∵ cos θ = (vecb.vecc)/(|vecb||vecc|))`

⇒ `(3)^2 + (4)^2 + 2 xx 3 xx 4 cos θ = (sqrt37)^2`

⇒ 9 + 16 + 24 cos θ = 37

⇒ 24 cos θ = 37 − 25

⇒ 24 cos θ = 12

⇒ cos θ = `1/2`

⇒ cos θ = `cos  pi/3`

∴ θ = `pi/3`