Question

Given below are two statements:

Assertion (A):
The angle between the pair of lines \[ \frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4} \quad \text{and} \quad \frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2} \] is \(\cos^{-1}\left(\frac{8\sqrt{3}}{15}\right)\).
Reason (R):
The angle between the two lines is \[ \cos\theta=\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}. \]

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

For angle between two lines in 3D, use direction ratios and apply the dot product formula.

Answer 1

The Correct Option is A