If the vectors 2i + j - k, , - i + 2j + k and - 5i + 2j - k are c… - Vidyadip

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

$\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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