Question

If the angle between the lines whose direction ratios are 2,-1 , 2 and a, 3, 5 be ${45}^{\circ }$, then a =

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D

4

$cos\theta =\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}\frac{1}{\sqrt{2}}=\frac{2a-3+10}{\sqrt{1^2+2^2+z^2}\sqrt{a^2+3^2+5^2}}\Rightarrow 9(a^2+34)=2[2a+7{]}^2=2[4a^2+28a+49]\Rightarrow a^2-56a+208=0\Rightarrow a=4.$