The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is ______.

Question

KollegeApply · Accepted Answer

The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is $90^\circ$. Explanation: 2x = 3y = – z 6x = – y = – 4z x/($\frac{1}{2}$) = y/($\frac{1}{3}$) = z/-1 x/($\frac{1}{6}$) = y/-1 = z/((-1)/4) Direction cosine's of both lines are ($\frac{1}{2}$, $\frac{1}{3}$, -1) and ($\frac{1}{6}$, -1, -$\frac{1}{4}$) respectively. (l1, m1, n1) = (3, 2, – 6) and (l2, m2, n2) = (2, – 12, – 3) cos $\theta$ = l1l2 + m1m2 + n1n2 = 6 – 24 + 18 = 0 \implies cos $\theta$ = 0 = cos $90^\circ$ $\therefore$ $\theta$ = $90^\circ$.

AChoose Your Answer