Geometry

3D Geometry

Medium

core

Let $(\alpha, 0, \beta)$ be the coordinates of the point, which divides the line segment joining the points (1,2,-3) and (1,-1,-4) internally, then $(\alpha^2+\beta^2)$ equals:

$\dfrac{130}{9}$

$\dfrac{132}{9}$

$\dfrac{132}{5}$

$\dfrac{129}{5}$

✅ Correct Option: 1

Let the ratio be $k:1$ . The $y$ -coordinate gives $\dfrac{-k+2}{k+1} = 0$ , so $k=2$ .

Then $\alpha = \dfrac{2(1)+1(1)}{3} = 1$ and $\beta = \dfrac{2(-4)+1(-3)}{3} = -\dfrac{11}{3}$ .

So $\alpha^2+\beta^2 = 1 + \dfrac{121}{9} = \dfrac{130}{9}$ .

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If the lines $\frac{x-1}{2} = \frac{y-m}{3} = \frac{z-3}{4}$ and $\frac{x-4}{5} = \frac{y-1}{2} = z$ are interesecting, then the value of $m$ , is

Let (α,0,β)(\alpha, 0, \beta)(α,0,β) be the coordinates of the point, which divides the line segment joining the points (1,2,-3) and (1,-1,-4) internally, then (α2+β2)(\alpha^2+\beta^2)(α2+β2) equals:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let $(\alpha, 0, \beta)$ be the coordinates of the point, which divides the line segment joining the points (1,2,-3) and (1,-1,-4) internally, then $(\alpha^2+\beta^2)$ equals: