Perform Operations with Vectors in Terms of i and j
-$\mathbf { v } = 10 \mathbf { i } + 9 \mathbf { j }$; Find $\| - 5 \mathbf { v } \|$.
A) $5 \sqrt { 181 }$
B) $5 \sqrt { 19 }$
C) $5 \mathrm { i } \sqrt { 19 }$
D) $- 5 \sqrt { 181 }$

Question

Quizplus · Accepted Answer

The magnitude of a vector $\mathbf{v} = ai + bj$ is given by $\|\mathbf{v}\| = \sqrt{a^2 + b^2}$. For $\mathbf{v} = 10i + 9j$, $\| - 5\mathbf{v} \| = |-5| \cdot \|\mathbf{v}\| = 5\sqrt{10^2 + 9^2} = 5\sqrt{100 + 81} = 5\sqrt{181}$.

Perform Operations with Vectors in Terms of I and J v=10i+9j\mathbf { v } = 10 \mathbf { i } + 9 \mathbf { j }v=10i+9j

Perform Operations with Vectors in Terms of I and J $\mathbf { v } = 10 \mathbf { i } + 9 \mathbf { j }$