Evaluate \(\left( 2\mathbf{i}+3\mathbf{j}-\mathbf{k} \right)\cdot \left( \mathbf{i}-5\mathbf{k} \rig

Question

Evaluate $\left( 2\mathbf{i}+3\mathbf{j}-\mathbf{k} \right)\cdot \left( \mathbf{i}-5\mathbf{k} \right)$. Evaluate $\left( \mathbf{i}-5\mathbf{j}+4\mathbf{k} \right)\cdot \left( 3\mathbf{i}-2\mathbf{j}-3\mathbf{k} \right)$. Evaluate $\left( -6\mathbf{i}+\mathbf{j} \right)\cdot \left( \mathbf{i}-\mathbf{j}-8\mathbf{k} \right)$. Find the acute angle between direction vectors $\left( 2\mathbf{i}+3\mathbf{j}-\mathbf{k} \right)$ and $\left( \mathbf{i}-5\mathbf{k} \right)$. Find the acute angle between direction vectors $\left( \mathbf{i}-5\mathbf{j}+4\mathbf{k} \right)$ and $\left( 3\mathbf{i}-2\mathbf{j}-3\mathbf{k} \right)$. Find the acute angle between direction vectors $\left( -6\mathbf{i}+\mathbf{j} \right)$ and $\left( \mathbf{i}-\mathbf{j}-8\mathbf{k} \right)$.

Accepted Answer

(a) $7$ (b) $1$ (c) $-7$ (d) $68.5^\circ$ (e) $88.1^\circ$ (f) $81.9^\circ$

Vectors - Scalar (Dot) Product

Vectors - Scalar (Dot) Product

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