A vector which is orthogonal to the vector ve | vedclass

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(A) Let the required vector be $\vec{v}$. Since $\vec{v}$ is coplanar with $\vec{b}$ and $\vec{c}$, it can be written as $\vec{v} = \vec{b} 	imes (\v

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$25\hat{i} + 19\hat{j} - 21\hat{k}$

Vedclass · Answer

(A) Let the required vector be $\vec{v}$. Since $\vec{v}$ is coplanar with $\vec{b}$ and $\vec{c}$, it can be written as $\vec{v} = \vec{b} 	imes (\vec{b} 	imes \vec{c})$ or simply as a linear combination $\vec{v} = \vec{b} 	imes (\vec{a} 	imes \vec{c})$ is not correct here. The vector coplanar to $\vec{b}$ and $\vec{c}$ and orthogonal to $\vec{a}$ is given by $\vec{v} = \vec{a} 	imes (\vec{b} 	imes \vec{c})$.First, calculate $\vec{b} 	imes \vec{c} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & 2 & 0 \ 2 & 1 & 3 \end{vmatrix} = \hat{i}(6-0) - \hat{j}(9-0) + \hat{k}(3-4) = 6\hat{i} - 9\hat{j} - \hat{k}$.Now, calculate $\vec{v} = \vec{a} 	imes (6\hat{i} - 9\hat{j} - \hat{k}) = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 2 & 3 \ 6 & -9 & -1 \end{vmatrix}$.$= \hat{i}(-2 - (-27)) - \hat{j}(-1 - 18) + \hat{k}(-9 - 12) = 25\hat{i} + 19\hat{j} - 21\hat{k}$.

$A$ vector which is orthogonal to the vector $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and coplanar with the vectors $\vec{b} = 3\hat{i} + 2\hat{j}$ and $\vec{c} = 2\hat{i} + \hat{j} + 3\hat{k}$ is

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