Question

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

Answer 1

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

given, $\vec{v_1}=2\hat{i}+3\hat{j}-\hat{k}$

$\vec{v_2}=\hat{i}+2\hat{j}-3\hat{k}$

concept : if two vectors A = $x_1\hat{i}+y_1\hat{j}+z_1\hat{k}$ and B = $x_2\hat{i}+y_2\hat{j}+z_2\hat{k}$

then, cross product of A and B = A × B = $(y_1z_2-y_2z_1)\hat{i}+(z_1x_2-z_2x_1)\hat{j}+(x_1y_2-x_2y_1)\hat{k}$

so, cross product of $\vec{v_1}$ and $\vec{v_2}$ = $\vec{v_1\times v_2}$

= $(3(-3)-(-1)2)\hat{i}+((-1)1-(-3)(2))\hat{j}+(2(2)-1(3))\hat{k}$

= $-7\hat{i}+5\hat{j}+\hat{k}$

Answer 2

$\huge\bold\purple{Answer:-}$

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}}}}