Question

For the two vectors $$\mathbf{A}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}, \quad \mathbf{B}=-2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}$$ find (a) $\mathbf{A}-\mathbf{B}$ and $|\mathbf{A}-\mathbf{B}|$ (b) component of B along A (c) angle between A and B (d) $\mathbf{A} \times \mathbf{B}$ (e) $(\mathbf{A}-\mathbf{B}) \times(\mathbf{A}+\mathbf{B})$

          For the two vectors
$$\mathbf{A}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}, \quad \mathbf{B}=-2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}$$
find (a) $\mathbf{A}-\mathbf{B}$ and $|\mathbf{A}-\mathbf{B}|$
(b) component of B along A
(c) angle between A and B
(d) $\mathbf{A} \times \mathbf{B}$
(e) $(\mathbf{A}-\mathbf{B}) \times(\mathbf{A}+\mathbf{B})$

Added by Mark M.

Instant Answer

Solved by Expert Ramesh Rajak

Step 1

$|\mathbf{A}-\mathbf{B}| = \sqrt{(3)^2 + (-1)^2 + (-2)^2} = \sqrt{14}$. Show more…

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For the two vectors $$\mathbf{A}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}, \quad \mathbf{B}=-2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}$$ find (a) $\mathbf{A}-\mathbf{B}$ and $|\mathbf{A}-\mathbf{B}|$ (b) component of B along A (c) angle between A and B (d) $\mathbf{A} \times \mathbf{B}$ (e) $(\mathbf{A}-\mathbf{B}) \times(\mathbf{A}+\mathbf{B})$