Question

If `hata_1,hata_2andhata_3`are unit vectors and`2hata_1+2hata_2+hata_3=0` then angle between `hata_1 and hata_2` is?

answer wrt sinh

Answer 1

`cos^-1(-7/8) ~~ 151^circ`

Explanation:

`hat a_3 = -2( hat a_1+hat a_2) implies`
`hat a_3^2 =4 (hat a_1+hat a_2)^2`
`qquad = 4 (hat a_1^2+hat a_2^2+2 hat a_1 cdot hat a_2) implies`
`1 = 4(1+1 +2 hat a_1 cdot hat a_2 ) implies`
`hat a_1 cdot hat a_2 = -7/8`

Thus, the angle `theta` between `hat a_1` and `hat a_2` is given by

`cos theta = (hat a_1 cdot hat a_2)/(|hat a_1| \ |hat a_2|)= -7/8` and thus

`theta = cos^-1(-7/8) ~~ 151^circ`