If the vectors 2i^^ −j^^+k^^, i^^+2j^^−3k^^, 3i^^+aj^^+5k^^ are coplanar, the a=

2−1112−33a5=0⇒2(10+3a)+14+a−6=0⇒7a+28=0⇒a=−4.

If the vectors 2i^^ −j^^+k^^, i^^+2j^^−3k^^, 3i^^+aj^^+5k^^ are coplanar, the a=

2−1112−33a5=0⇒2(10+3a)+14+a−6=0⇒7a+28=0⇒a=−4.

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If the vectors $2 \overset{}{\hat{\hat{i}}} - \hat{\hat{j}} + \hat{\hat{k}}, \hat{\hat{i}} + 2 \hat{\hat{j}} - 3 \hat{\hat{k}}, 3 \hat{\hat{i}} + a \hat{\hat{j}} + 5 \hat{\hat{k}}$ are coplanar, the $a =$

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$|\begin{array}{ccc} 2 & - 1 & 1 \\ 1 & 2 & - 3 \\ 3 & a & 5 \end{array}| = 0 \Rightarrow 2 (10 + 3 a) + 14 + a - 6 = 0$
$\Rightarrow 7 a + 28 = 0 \Rightarrow a = - 4$ .

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If the vectors 2i^^ −j^^+k^^, i^^+2j^^−3k^^, 3i^^+aj^^+5k^^ are coplanar, the a=

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If the vectors $2 \overset{}{\hat{\hat{i}}} - \hat{\hat{j}} + \hat{\hat{k}}, \hat{\hat{i}} + 2 \hat{\hat{j}} - 3 \hat{\hat{k}}, 3 \hat{\hat{i}} + a \hat{\hat{j}} + 5 \hat{\hat{k}}$ are coplanar, the $a =$