Question

find the vector product axb.if a=i+2j-k and b=2i+3j+k?
a)5i-3j-k
b)2i-4j-k
c)3i+j-k
d)I-j+3k

Answer 1

Answer on Question #59691 – Math – Analytic Geometry

Question

1. Find the vector product $\mathbf{a} \times \mathbf{b}$, if $\mathbf{a} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $\mathbf{b} = 2\mathbf{i} + 3\mathbf{j} + \mathbf{k}$?

a) $5\mathbf{i} - 3\mathbf{j} - \mathbf{k}$

b) $2\mathbf{i} - 4\mathbf{j} - \mathbf{k}$

c) $3\mathbf{i} + \mathbf{j} - \mathbf{k}$

d) $\mathbf{i} - \mathbf{j} + 3\mathbf{k}$

Solution

$$\begin{array}{l} \mathbf{a} \times \mathbf{b} = \left| \begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & -1 \\ 2 & 3 & 1 \end{array} \right| = (2 \cdot 1 - 3 \cdot (-1)) \mathbf{i} - (1 \cdot 1 - 2 \cdot (-1)) \mathbf{j} + \\ + (1 \cdot 3 - 2 \cdot 2) \mathbf{k} = (2 + 3) \mathbf{i} + (-2 - 1) \mathbf{j} + (3 - 4) \mathbf{k} = 5\mathbf{i} - 3\mathbf{j} - \mathbf{k}. \end{array}$$

Thus, a) $5\mathbf{i} - 3\mathbf{j} - \mathbf{k}$ is a correct answer.

**Answer:** a) $5\mathbf{i} - 3\mathbf{j} - \mathbf{k}$.

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