MHT CET · Maths · Straight Lines
The acute angle between the lines
\(x=-2+2 \mathrm{t}, \mathrm{y}=3-4 \mathrm{t}, \mathrm{z}=-4+\mathrm{t}\) and \(x=-2-\mathrm{t}, \mathrm{y}=3+2 \mathrm{t}, \mathrm{z}=-4+3 \mathrm{t}\) is
- A \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\)
- B \(\cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\)
- C \(\sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\)
- D \(\cos ^{-1}\left(\frac{2}{\sqrt{6}}\right)\)
Answer & Solution
Correct Answer
(A) \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\)
Step-by-step Solution
Detailed explanation
\(\vec{v_1} = \langle 2, -4, 1 \rangle, \vec{v_2} = \langle -1, 2, 3 \rangle\) \(\vec{v_1} \cdot \vec{v_2} = (2)(-1) + (-4)(2) + (1)(3) = -2 - 8 + 3 = -7\)
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