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The value of $m$, if the vectors $\hat{\imath}-\hat{\jmath}-6 \hat{k}, \hat{\imath}-3 \hat{\jmath}+4 \hat{k}$ and $2 \hat{\imath}-5 \hat{\jmath}+m \hat{k}$ are
coplanar, is
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coplanar, is
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2848 Upvotes
Verified Answer
The correct answer is:
3
$\bar{a}=\hat{i}-\hat{j}-6 \hat{k}, \bar{b}=\hat{i}-3 \hat{j}+4 \hat{k}, \bar{c}=2 \hat{i}-5 \hat{j}+m \hat{k}$ are coplanar
$\begin{aligned}
\therefore &\left|\begin{array}{rrr}
1 & -1 & -6 \\
1 & -3 & 4 \\
2 & -5 & \mathrm{~m}
\end{array}\right|=0 \\
& 1(-3 \mathrm{~m}+20)+1(\mathrm{~m}-8)-6(-5+6)=0 \\
&-3 \mathrm{~m}+20+\mathrm{m}-8+30-36=0 \Rightarrow-2 \mathrm{~m}+6=0 \quad \Rightarrow \mathrm{m}=3
\end{aligned}$
$\begin{aligned}
\therefore &\left|\begin{array}{rrr}
1 & -1 & -6 \\
1 & -3 & 4 \\
2 & -5 & \mathrm{~m}
\end{array}\right|=0 \\
& 1(-3 \mathrm{~m}+20)+1(\mathrm{~m}-8)-6(-5+6)=0 \\
&-3 \mathrm{~m}+20+\mathrm{m}-8+30-36=0 \Rightarrow-2 \mathrm{~m}+6=0 \quad \Rightarrow \mathrm{m}=3
\end{aligned}$
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