Question

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

Explanation:

Step1: Find the scalar multiple \( cu \)

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

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

The magnitude of a vector \( \langle x, y
angle \) is given by \( \|\langle x, y
angle\| = \sqrt{x^2 + y^2} \). For \( c\mathbf{u} = \langle -15, 36
angle \):
\[
\|c\mathbf{u}\| = \sqrt{(-15)^2 + 36^2} = \sqrt{225 + 1296} = \sqrt{1521} = 39
\]
(Note: The magnitude of a vector is always non - negative, so we can also use the property \( \|c\mathbf{u}\| = |c| \|\mathbf{u}\| \). First, find \( \|\mathbf{u}\|=\sqrt{5^2+(-12)^2}=\sqrt{25 + 144}=\sqrt{169} = 13 \). Then \( \|c\mathbf{u}\|=| - 3|\times13=3\times13 = 39 \))

Answer:

39