If (2 ,-1 ,2 ) and (K ,3 ,5 ) are the triads of direction ratios of two lines and the angle between them is 45^ , then the value of K is

Question

Accepted Answer

Correct answer: C. (c) Given direction ratios are (2 ,-1 ,2 ) and (K ,3 ,5 ) Let be thection ratios are (2 ,-1 ,2 ) and (K ,3 ,5 ) be the angle between two lines, then cos ⁡ = (2 ,-1 ,2 ) (K ,3 ,5 ) 4+1+4 K^2+9+25 cos ⁡45^ = 2K-3+10 9 K^2+34 1 2= 2K+73 K^2+9+253 K^2+34= 2 (2K+7 )9(K^2+34)=2 (2K+7 )^29K^2+306=8K^2+56K+98K^2-56K+208=0 ⇒K=52 ,4 ∴ According to the given options, K=4

$If (2, - 1, 2) and (K, 3, 5) are the triads of direction ratios of two lines and the angle between them is 45^{\circ}, then the value of K is$

Solution

More Three-Dimensional Geometry PYQs