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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2024 · Mathematics · Three Dimensional Geometry

The magnitude of projection of line joining (3,4 , 5) and (4,6,3)...

The magnitude of projection of line joining (3,4(3,4, 5)5) and (4,6,3)(4,6,3) on the line joining (−1,2,4)(-1,2,4) and (1,0,5)(1,0,5) is

Options

  1. A43\frac{4}{3}
  2. B23\frac{2}{3}
  3. C83\frac{8}{3}
  4. D13\frac{1}{3}

Correct answer

A. 43\frac{4}{3}

Step-by-step solution

We know that, projection of a\mathbf{a} on b\mathbf{b} is given by projection, ∣a∣cos⁡θ=(a⋅b)∣b∣|\mathrm{a}| \cos \theta=\frac{(\mathbf{a} \cdot \mathbf{b})}{|\mathbf{b}|} Let line joining points (3,4,5)and(4,6,3)(3,4,5) and (4,6,3) is L1L_1 and line joining points (−1,2,4)and(1,0,5)(-1,2,4) and (1,0,5) is L2⇒L_2\Rightarrow \quadL1=i^+2j^−2k^L2=2i^−2j^+k^\begin{aligned} & L_1=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}} \\ & L_2=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}} \end{aligned}∴\therefore Projection of L1andL2=L1⋅L2∣L2∣=2−4−24+4+1=−43∴L_1 and L_2=\frac{L_1 \cdot L_2}{\left|L_2\right|}=\frac{2-4-2}{\sqrt{4+4+1}}=\frac{-4}{3}\therefore Magnitude =43\frac{4}{3}
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