Question

. r = i-2j+2k and p = 4j -3k find the vector product i.e r X p​

Answer 1

Answer:

-2i+3j+4k take the determinant of two vectors since I component in p is zero p=0i+4j-3k

Answer 2

The cross product is $\vec{r} \times \vec{p} = -2 \hat{i} + 3 \hat{j} + 4 \hat{k}$

Step-by-step Explanation:

Given: $\vec{r} = \hat{i} -2 \hat{j} + 2 \hat{k}$ and $\vec{p} = 4 \hat{j} - 3 \hat{k}$

To Find: cross product $\vec{r} \times \vec{p}$

Solution:

• Finding the cross product $\vec{r} \times \vec{p}$

The cross product of the given vectors is;

$\vec{r} \times \vec{p} = \begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\1&-2&2\\0&4&-3\end{vmatrix}$

$\Rightarrow \vec{r} \times \vec{p} = \hat{i} [(-2)(-3) - (4)(2)] - \hat{j} [(1)(-3) - (0)(2)] + \hat{k} [(1)(4) - (0)(-2)]$

$\Rightarrow \vec{r} \times \vec{p} = \hat{i} [6 - 8] - \hat{j} [-3-0] + \hat{k} [4 - 0]$

$\Rightarrow \vec{r} \times \vec{p} = -2 \hat{i} + 3 \hat{j} + 4 \hat{k}$

Hence, the cross product is $\vec{r} \times \vec{p} = -2 \hat{i} + 3 \hat{j} + 4 \hat{k}$