Find the magnitude.
-Let $\mathbf { u } = \langle - 1,2 \rangle$. Find the magnitude (length) of the vector: $7 \mathbf { u }$.
A) $7 \sqrt { 10 }$
B) $- 7 \sqrt { 5 }$
C) $7 \sqrt { 5 }$
D) $\sqrt { 10 }$

Question

Quizplus · Accepted Answer

To find the magnitude of a vector, we use the formula:

$$\left\Vert \mathbf {v} \right\Vert = \sqrt{v_1^2+v_2^2}$$

where $\mathbf{v} = \langle v_1,v_2 \rangle$.

In this case, we want to find the magnitude of $7\mathbf{u}$.

$$\left\Vert 7\mathbf{u} \right\Vert = \sqrt{(7u_1)^2 + (7u_2)^2} = \sqrt{7^2 \cdot (u_1^2 + u_2^2)} = 7\sqrt{(-1)^2 + 2^2} = 7\sqrt{5}$$

Therefore, the answer is (C) $7\sqrt{5}$.

Find the Magnitude u=⟨−1,2⟩\mathbf { u } = \langle - 1,2 \rangleu=⟨−1,2⟩

Find the Magnitude $\mathbf { u } = \langle - 1,2 \rangle$