Let $\mathbf{u}= (a,2,-1)$ and $\mathbf{v}= (3,b,4)$ be vectors in $\mathbb{R}^3$ such that $\mathbf{u}$ is perpendicular to $\mathbf{v}$ and $|\mathbf{u}| = 6$. Given that $a0$, find the ordered pair $(a,b)$.

Question

Let $\mathbf{u}= (a,2,-1)$ and $\mathbf{v}= (3,b,4)$ be vectors in $\mathbb{R}^3$ such that $\mathbf{u}$ is perpendicular to $\mathbf{v}$ and $|\mathbf{u}| = 6$. Given that $a>0$, find the ordered pair $(a,b)$.

Accepted Answer

(\sqrt{31}, \frac{4-3\sqrt{31}}{2})

Neco 2019 Further Mathematics Question 11

Let \(\mathbf{u}= (a,2,-1)\) and \(\mathbf{v}= (3,b,4)\) be vectors in \(\mathbb{R}^3\) such that \(\mathbf{u}\) is perpendicular to \(\mathbf{v}\) and \(|\mathbf{u}| = 6\). Given that \(a>0\), find the ordered pair \((a,b)\).

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