Question

The plane passing through the point $(-2,-2,2)$ and containng the line joining the points $(1,1,1)$ & $(,1,-1,2)$ makes intercept of length $a,b,c$ an aes of $x,y,z$ respectively then

• A. $a=3b$
• B. $a+b+c=12$
• C. No. of ways to distribute $(3b+6c)$ alike objects among $\frac{a}{2}$ boys =${}^{19}{C}_4$
• D. $\tan \left(\frac{\pi (b+c)}{2a}\right)=1$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $a=3b$
B $a+b+c=12$
C No. of ways to distribute $(3b+6c)$ alike objects among $\frac{a}{2}$ boys =${}^{19}{C}_4$

since $a=$ length of $x$ - intercept $=8$
$b=$ length $y$ - = $\frac{8}{3}$
$C=$ length =$\frac{8}{6}$
A) $a=3b$
B) $b+b+c=8+\frac{8}{3}+\frac{8}{6}=12$
c) $3b+6c=16$ $\frac{a}{2}=\frac{8}{2}=4$

Then ways ${}^{16+4-1}{C}_4{=}^{19}{C}_4$