Question

Determine the vector product of v⃗ 1=2i∧+3j∧−k∧v→1=2i∧+3j∧−k∧ and v⃗ 2=i∧+2j∧−3k∧,​

Answer 1

Correct question.

Determine the vector product of

$\large{\bold{ \vec{V_1} = 2 \hat{i} + 3 \hat{j} - \hat{k}}}$

$\large{\bold{ \vec{V_2} = \hat{i} + 2 \hat{j} - 3\hat{k}}}$

$\huge{\bold{\underline{Given:-}}}$

$\large{\bold{ \vec{V_1} = 2 \hat{i} + 3 \hat{j} - \hat{k}}}$

$\large{\bold{ \vec{V_2} = \hat{i} + 2 \hat{j} - 3\hat{k}}}$

$\huge{\bold{\underline{Explanation:-}}}$

Here,

$V_1 \times V_2 = \left[ \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 3 & 3 & -1 \\ 1 & 2 & -3 \end{array} \right]$

Now,

${ \implies V_1 \times V_2 = \hat{i}( - 9 - (-2)) + \hat{j}(-1 - ( -9)) + \hat{k}(6 - 3)}$

Simplifying

${ \implies V_1 \times V_2 = \hat{i}( - 7) + \hat{j}(8) + \hat{k}(3)}$

$\large{\boxed{\boxed{ V_1 \times V_2 = -7 \hat{i} + 8 \hat{j} + 3\hat{k}}}}$