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The line segment joining the points \(A(2,3,4)\) and \(B(-3,5,-4)\) intersects \(y z\)-plane at the point
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Verified Answer
The correct answer is:
\(\left(0, \frac{19}{5}, \frac{4}{5}\right)\)
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.
\(M\left(\frac{-3 \lambda+2}{\lambda+1}, \frac{5 \lambda+3}{\lambda+1}, \frac{-4 \lambda+4}{\lambda+1}\right)\)
\(\because\) 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.
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