Question

A plane which passes through the point $(3,2,0)$ and the line $\frac{x-4}{1}=\frac{y-7}{5}=\frac{z-4}{4}$ is?

• A. $x-y+z=1$
• B. $x+y=z=5$
• C. $x+2y-z=1$
• D. $2x-y+z=5$

Answer 1

The correct option is A $x-y+z=1$

Given that, plane through $(3,2,0)$ and the line $\frac{x-4}{1}=\frac{y-7}{5}=\frac{z-4}{4}$

Equation of plane passing through $(3,2,0)$ is of form $a(x-3)+b(y-2)+c(z-0)=0...eq.1$

The given line passes through $(3,2,0)$ and has the D.R's $(1,5,4)$

The line also passes through point $(4,7,4)$

As plane 1 contains this point, we have

$a(4-3)+b(7-2)+c(4-0)=0\Rightarrow a+5b+4c=0....eq.2$

As the direction ratios are $(1,5,4)$ , we have.

$a\left(1\right)+b\left(5\right)+c\left(4\right)=0\Rightarrow a+5b+4c=0...eq.3$

From eq.2 and eq.3 equations, we can't calculate the D.R's as both are same equations.

Hence this question is not solvable as proper values are not present in question.