Maths · Direction ratios and direction cosines and the angle between two intersecting lines
If is the angle between the lines where are the three points with coordinates (1
If \( \theta \) is the angle between the lines \( A B, A C \) where \( A, B, C \) are the three points with coordinates (1,2,-1),(2,0,3),(3,-1,2) respectively, then \( \sqrt{462} \cos \theta \) is equal to
- A. 20
- B. 2
- C. 22
- D. 26
Step-by-step solution
Vectors AB=(1,-2,4), AC=(2,-3,3). Dot product=20, magnitudes √21 and √22, so cosθ=20/√462. Hence √462 cosθ=20.
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