Question

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

• A. $0$
• B. $-1$
• C. $-5$
• D. $5$

Answer 1

The correct option is B $-1$

Given: $A=(3,1,-2),B=(-1,0,1)$
Direction ratios of $AB$ are:
$(3+1,1-0,-2-1)$ i.e. $(4,1,-3)$
Projection of $AB$ on $x$-axis $\overrightarrow{AB}\cdot \hat{i}=a_x=4$
Projection of $AB$ on $y$-axis $\overrightarrow{AB}\cdot \hat{j}=a_y=l=1$
Projection of $AB$ on $z$-axis $\overrightarrow{AB}\cdot \hat{k}=a_z=-3$
Projection of $AB$ on $zx$ plane $=\sqrt{a_x^2+a_z^2}=\sqrt{4^2+3^2}=5$
$3l^2-m+1=3\times 1-5+1=-1$