Question

A plane $x-3y+5z=d$ passes through the point $(1,2,4)$. Intercepts on the axes are

• A. $15,-5,3$
• B. $1,-5,3$
• C. $-15,5,-3$
• D. $1,-6,20$

Answer 1

Answer: (A)

$15,-5,3$

$(1,2,4)$ must satisfy this plane

$\left(1\right)\left(1\right)-\left(3\right)\left(2\right)+\left(5\right)\left(4\right)=d$

$\Rightarrow$ \plane $\Rightarrow x-3y+5z=15$

x intercept $\Rightarrow x-0+0=15\Rightarrow 15=xml$

y intercept $\Rightarrow 0-3y+0=15\Rightarrow yint=-5$

z intercept $\Rightarrow 0-0+52=15\Rightarrow zint.=3$

$\therefore A=(15,-5,3)$