If ` |vec A|=2 and | vec B| =4` , then match the relations in colum I with theange ` theta` between `vec A and vec B` in column II.
Column I , Column II
(a) ` vec A.vec B=0` , (i) ` theta` =0`
(b) ` vec A . Vec B= + 8` , (ii) ` theta =90^@`
(c ) ` vec A .vec B =4` , (iii) ` theta =180^@`
(d) ` vec A .vec B =- 8` , (iv) ` theta =60^@`.

Explanation

Given ` | vec A | =2, |vec B| =4`
` 9a) ` vec A. vec B =0 = AB cos theta = 2 xx 4 cos theta`
or ` 0= 8 cos theta or cos thera =0 or theta = 90^@`. It matches with option (ii).
(b) ` vec A.vec B =4 = AB cos theta =2 xx 4 xx cos theta or cos thera = 1, theta =0^@`. It matches with option (i)
(C )` vec A. vec B =4 = AB cos thera =2 xx 4 xx cos or cos theta = 1/2 or thate =60&@`. It matches with option (iv).
(d) ` vec A .vec B =-8 = 2 xx 4 cos thera or cos thera =- 1 or theta 180^@`. It matches with option (iii).