Vectors $\mathbf{A}=\langle 3,-4,2\rangle$ and $\mathbf{B}=\langle k,1,-1\rangle$ satisfy $|\mathbf{A}+\mathbf{B}|=10$. Find the value of $k$ that gives an acute angle between $\mathbf{A}$ and $\mathbf{B}$, and compute that acute angle (to the nearest degree).

Question

Accepted Answer

k = -3 + 3√10; acute angle ≈ 68°

Neco 2020 Further Mathematics Question 25

Vectors \(\mathbf{A}=\langle 3,-4,2\rangle\) and \(\mathbf{B}=\langle k,1,-1\rangle\) satisfy \(|\mathbf{A}+\mathbf{B}|=10\). Find the value of \(k\) that gives an acute angle between \(\mathbf{A}\) and \(\mathbf{B}\), and compute that acute angle (to the nearest degree).

Answer Options

About This Question

Master the Exam!