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VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA3 Marks
Question
Find the value of $\lambda$ which makes the vectors $\vec{a},\vec{b},\vec{c}$ coplanar, where $\vec{a}=-4\hat{\text{i}}-6\hat{\text{j}}-2\hat{\text{k}},\text{ }\vec{b}=-\hat{\text{i}}+4\hat{\text{j}}+3\hat{\text{k}}$ and  $\vec{c}=-8\hat{\text{i}}-\hat{\text{j}}+\lambda\hat{\text{k}.}$
✓

Answer

For coplanarity $[\vec{a},\vec{b},\vec{c}]=0$$\therefore\begin{vmatrix} -4 & -6 & -2 \\ -1 & 4 & 3 \\ -8 & -1 & \lambda \end{vmatrix}=0$
$\Rightarrow$ – 8 (–18 + 8) + (–12 – 2) + $\lambda$ (–16 – 6) = 0
$\Rightarrow$ 80 – 14 – 22 $\lambda$ = 0 ​​$\Rightarrow$ $\lambda$ = 3.

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