Question

Given that $\overline{a},\overline{b},\overline{c}$ is a triad of three non-coplanar vectors such that

$(2h+k)\overline{a}+(3-4h+l)\overline{b}+(1+h+k)\overline{c}=h\overline{a}+k\overline{b}+l\overline{c}$. Find $h,k$ and $l$.

• A. $h=4/3,k=-2/3,l=3.$
• B. $h=5/3,k=-4/3,l=3.$
• C. $h=4/3,k=-4/3,l=1.$
• D. $h=5/3,k=-2/3,l=1.$

Answer 1

The correct option is C $h=4/3,k=-4/3,l=1.$

Given $\overline{a},\overline{b},\overline{c}$ is a triad of three non-coplanar vectors.

$(2h+k)\overline{a}+(3-4h+l)\overline{b}+(1+h+k)\overline{c}=h\overline{a}+k\overline{b}+l\overline{c}$.

comparing coefficients on both sides gives

$h+k=0$ -----(1)

$4h+k-l=3$ ----(2)

$h+k-l=-1$ ----(3)

from (1) and (3) $l=1$

solving (1) and (2) for $h,k$ gives $h=\frac{4}{3}$ and $k=\frac{-4}{3}$

$\therefore h=\frac{4}{3},k=\frac{-4}{3},l=1$

Hence, option C.