XY - plane divides the line joining the points A 2-3-5 and B -1-2-3 in the ratioA- 5-3 InternallyB- 2- 1 InternallyC- 5- 3 ExternallyD- 3-2 Externally

The correct option is C 5:3 ExternallyEquation of XY plane is z=0 Let nbsp; plane cuts nbsp; the line joining the points in the ratio k:1 at the point P(x, ...

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Standard XII

Mathematics

Section Formula

XY - plane di...

Question

$X Y$ – plane divides the line joining the points $A (2, 3, - 5)$ and $B (- 1, - 2, - 3)$ in the ratio

5:3 Internally

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2:1 Internally

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5:3 Externally

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3:2 Externally

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Solution

The correct option is C 5:3 Externally
Equation of XY-plane is $z = 0$
Let plane cuts the line joining the points in the ratio $k : 1$ at the point $P (x, y, z)$
$z = \frac{- 3 k - 5}{k + 1} = 0 \Rightarrow - 3 k = 5 \Rightarrow k = \frac{- 5}{3}$
The negative sign infer that the plane cuts the line externally in the ratio
$\frac{5}{3}$ externally

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XY – plane divides the line joining the points A (2,3,−5) and B (−1,−2,−3) in the ratio

The correct option is C 5:3 ExternallyEquation of XY-plane is z=0 Let plane cuts the line joining the points in the ratio k:1 at the point P(x,y,z) z=−3k−5k+1=0⇒−3k=5⇒k=−53 The negative sign infer that the plane cuts the line externally in the ratio 53 externally

$X Y$ – plane divides the line joining the points $A (2, 3, - 5)$ and $B (- 1, - 2, - 3)$ in the ratio