Question

The angle between the straight lines $\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}$ and $\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}$ is

• A. ${45}^0$
• B. ${30}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

The correct option is D ${90}^0$

The direction ratios of the lines are $a_1=2,b_1=5,c_1=4,a_2=1,b_2=2,c_2=-3$

Thus $\cos \theta =\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{{\left(a_1\right)}^2+{\left(b_1\right)}^2+{\left(c_1\right)}^2}\sqrt{{\left(a_2\right)}^2+{\left(b_2\right)}^2+{\left(c_2\right)}^2}}$

$\Rightarrow \cos \theta =\frac{2\times 1+5\times 2+4\times -3}{\sqrt{{\left(2\right)}^2+{\left(5\right)}^2+{\left(4\right)}^2}\sqrt{{\left(1\right)}^2+{\left(2\right)}^2+{(-3)}^2}}=0$

$\Rightarrow \theta ={\cos }^{-1}0=\frac{\pi }{2}$