MCQ
If the vectors $2i + j - k,\, - i + 2j + \lambda k$ and $ - 5i + 2j - k$ are coplanar, then the value of $\lambda $ is equal
- A$-13$
- B$13/9$
- ✓$-13/9$
- D$-9/13$
✓
Answer
Correct option: C.
$-13/9$
c
(c) Given vectors are coplanar
(c) Given vectors are coplanar
$\therefore $ $\left| {\begin{array}{*{20}{c}}2&1&{ - 1}\\{ - 1}&2&\lambda \\{ - 5}&2&{ - 1}\end{array}} \right| = 0$
==> $ - 4 - 4\lambda - 5\lambda - 1 - 8 = 0$
==> $ - 9\lambda - 13 = 0$ ==> $\lambda = \frac{{ - 13}}{9}$.
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