Question

lf $A=(3,1,-2),B=(-1,0,1)$ and $l,m$ are the projections of $AB$ on the $y$-axis, $zx$-plane respectively, then $3l^2-m+1=$

• A. $-1$
• B. $0$
• C. $1$
• D. $9$

Answer 1

The correct option is A $-1$

Given $A=(3,1,-2),B=(-1,0,1)$

DR's of $AB$ are $(3-(-1),1-0,-2-1)$

$\overrightarrow{AB}=(4,1,-3)$ or $(4\hat{i}+\hat{j}-3\hat{k})$

Projection of $AB$ on $x-$ axis is $\overrightarrow{AB}.\hat{i}$

$a_x=4$

Projection of $AB$ on $y-$ axis is $\overrightarrow{AB}.\hat{j}$

$l=a_y=1$

Projection of $AB$ on $z-$ axis is $\overrightarrow{AB}.\hat{k}$

$a_z=-3$

Projections of $\overrightarrow{AB}$ on $zx$ plane $=\sqrt{{a_x}^2+{a_z}^2}$

$=\sqrt{4^2+3^2}=5$

$3l^2-m+1=3\times 1-5+1=-1$