Question

The co-ordinate of a point where the line $(2,-3,1)$ and $(3,-4,-5)$ cuts the plane $2x+y+z=7$ are $(1,k,7)$ then value of $k$ equals

• A. $1$
• B. $-2$
• C. $2$
• D. None of these

Answer 1

Answer: (B)

$-2$

We know that the equation of the line passing through the point $(x_1,y_1,z_1),(x_2,y_2,z_2)$

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

Now the given line passes through the points $(2,-3,1),(3,-4,-5)$

Hence the equation of the line is $\frac{x-2}{3-2}=\frac{y+3}{-4+3}=\frac{z-1}{-5-1}$

`

= $\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}$

Let the above equation be equal to :

$\frac{x-2}{1}=1$ .... (1)

$\frac{y+3}{-1}=a$ .....(2)

$\frac{z-1}{-6}=7$ .....(3)

$\Rightarrow$ from eqn (2)

$y=-4+a$

cube cuts the plane $2x+y+z=7$ ... (4)

substitute the $(1,k,7)$ in eqn (4)

$2\left(1\right)+(-4+a)+7=7$

$a=2$

substitute a value in $y=-4+a$

we get $y=-4+2=-2$

hence the ans will be $(1,-2,7)$