Maths · Direction ratios and direction cosines and the angle between two intersecting lines
The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose
The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose direction ratios are 2,-3,6 is
- A. 28
- B. 4
- C. \( \frac{40}{7} \)
- D. \( \sqrt{45} \)
Step-by-step solution
The vector from (0,0,0) to (5,2,4) is v = (5,2,4). The direction vector of the line is d = (2,-3,6). The projection length of v onto d is |v·d|/|d|. Compute v·d = 5×2 + 2×(-3) + 4×6 = 10 - 6 + 24 = 28. |d| = √(2²+(-3)²+6²) = √(4+9+36)=√49=7. So projection = 28/7 = 4.
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