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Question: The angle between the pair of lines with direction ratios (1, 1, 2) and \(( \sqrt { 3 } - 1 , - \sq...

The angle between the pair of lines with direction ratios

(1, 1, 2) and (3−1,−3−1,4)( \sqrt { 3 } - 1 , - \sqrt { 3 } - 1,4 ) is

A

30∘30 ^ { \circ }

B

45∘45 ^ { \circ }

C

60∘60 ^ { \circ }

D

90∘90 ^ { \circ }

Answer

60∘60 ^ { \circ }

Explanation

Solution

cos⁡θ=1(3−1)−1(3+1)+2×4624=612⇒θ=60∘\cos \theta = \frac { 1 ( \sqrt { 3 } - 1 ) - 1 ( \sqrt { 3 } + 1 ) + 2 \times 4 } { \sqrt { 6 } \sqrt { 24 } } = \frac { 6 } { 12 } \Rightarrow \theta = 60 ^ { \circ }.