Given that $\mathbf{a}\times\mathbf{b}=\mathbf{0}$, what can be deduced about the vectors \(\

Question

Given that $\mathbf{a}\times\mathbf{b}=\mathbf{0}$, what can be deduced about the vectors $\mathbf{a}$ and $\mathbf{b}$?[2] Find a unit vector $\mathbf{n}$ such that $\mathbf{n}\times(2\mathbf{i}-\mathbf{j}+3\mathbf{k})=\mathbf{0}$.[1] Find the cosine of the acute angle between $2\mathbf{i}-\mathbf{j}+3\mathbf{k}$ and the $y$-axis.[2]

Accepted Answer

(a) parallel, or at least one is the zero vector (b) $\mathbf n=\pm\dfrac1{\sqrt{14}}(2,-1,3)$ (c) $\dfrac1{\sqrt{14}}$

2025 EJC Promo Q3

2025 EJC Promo Q3

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