Question

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

Answer 1

QUESTION:

$\vec{r} = \hat{i}-2\hat{j}+2\hat{k} \ and\ \vec{p} = 4\hat{j} -3\hat{k} \ Find\ the\ vector\ product\ i.e\ x\times p$

ANSWER:

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

GIVEN:

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

TO FIND:

• The vector product.

EXPLANATION:

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

$\vec{p} = 4\hat{j} -3\hat{k}$

$\vec{A} \times \vec{B} = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\x_1&y_1&z_1\\x_2&y_2&z_2\end{array}\right|$

$\vec{r} \times \vec{p} = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\1&-2&2\\0&4&-3\end{array}\right|$

$\vec{r} \times \vec{p} = \hat{i}((-2\times -3)-4\times2)-\hat{j}((1\times -3)+0)+\hat{k}(1\times 4 + 0)$

$\vec{r} \times \vec{p} = \hat{i}(6-8)-\hat{j}(-3)+\hat{k}(4)$

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

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

CROSS PRODUCT:

• The cross product of two vectors always result in a vector.

• Cross product is also known as vector product as gives result as a vector.

• Another formula for vector product is A × B = AB sin θ.

DOT PRODUCT:

• The dot product of two vectors always result in a scalar.

• Dot product is also known as scalar product as gives result as a scalar.

• Formula for scalar product is A . B = AB cos θ.