If hata_1,hata_2andhata_3 are unit vectors and2hata_1+2hata_2+hata_3=0 then angle between hata_1 and hata_2 is?

answer wrt sinh

1 Answer
Jun 23, 2018

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