Question

Given two vectors A⃗ =4.00i^+7.00j^ and B⃗ =5.00i^−2.00j^ , find the vector product A⃗ ×B⃗ (expressed in unit vectors).

Answer 1

Answer:

$-43\hat{k}$

Explanation:

given,

$\vec{A} = 4 \hat{i} + 7 \hat{j}$

$\vec{B} = 5 \hat{i} - 2 \hat{j}$

vector product $\vec{A} \times \vec{B} = ?$

$\vec{A} \times \vec{B}$ = $\begin{bmatrix}i & j & k\\ 4 & 7 &0 \\ 5 & -2 & 0\end{bmatrix}$

now, expanding the vector

$\vec{A} \times \vec{B}= \hat{k}(-2\times 4 - 7\times 5)$

$\vec{A} \times \vec{B}= -43\hat{k}$

the vector product is equal to $-43\hat{k}$