Q106 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

The line segment joining the points \(A(2,3,4)\) and \(B(-3,5,-4)\) intersects \(y z\)-plane at the point

  • Correct answer
    A
    \(\left(0, \frac{19}{5}, \frac{4}{5}\right)\)
  • B
    \((0,4,5)\)
  • C
    \(\left(9, \frac{14}{5}, 4\right)\)
  • D
    \((0,0,0)\)

Solution

Let \(y z\)-plane intersects the line joining points \(A(2,3,4)\) and \(B(-3,5,-4)\) in the ratio \(\lambda: 1\) at point \(M\), then \(M\left(\frac{-3 \lambda+2}{\lambda+1}, \frac{5 \lambda+3}{\lambda+1}, \frac{-4 \lambda+4}{\lambda+1}\right)\) \(\because\) On \(y z\)-plane, \(x\)-coordinate \(=0\) \(\Rightarrow \quad \lambda=2 / 3\) So, point \(M\) have coordinates \(\left(0, \frac{19}{5}, \frac{4}{5}\right)\) Hence, option (a) is correct.

Hence, the correct answer is option: 'A'.

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