Question

let \\( \mathbf{u} = \langle 5, -12 \
angle \\) and \\( c = -3 \\). what is \\( \\| c\mathbf{u} \\| \\)?
51 -39 39 21

Explanation:

Step1: Find \( c\mathbf{u} \)

Given \( \mathbf{u}=\langle 5, - 12
angle \) and \( c=-3 \), we multiply each component of \( \mathbf{u} \) by \( c \). So \( c\mathbf{u}=\langle - 3\times5,-3\times(-12)
angle=\langle - 15,36
angle \).

Step2: Calculate the magnitude of \( c\mathbf{u} \)

The magnitude of a vector \( \langle x,y
angle \) is given by \( \sqrt{x^{2}+y^{2}} \). For \( c\mathbf{u}=\langle - 15,36
angle \), the magnitude \( \|c\mathbf{u}\|=\sqrt{(-15)^{2}+36^{2}}=\sqrt{225 + 1296}=\sqrt{1521}=39 \).

Answer:

39