Question

given the following vectors, calculate $-7v$.
$u = \langle 6, -8 \
angle, v = \langle 6, -5 \
angle$

Explanation:

Step1: Multiply each component of vector \(v\) by \(-7\)

Given \(v=\langle6,-5
angle\), then \(-7v=-7\times\langle6,-5
angle\)
Using the scalar - vector multiplication rule \(k\langle a,b
angle=\langle ka,kb
angle\) (where \(k = - 7\), \(a = 6\), \(b=-5\)), we have:
\(-7v=\langle-7\times6,-7\times(-5)
angle\)

Step2: Calculate the components

For the \(x\) - component: \(-7\times6=-42\)
For the \(y\) - component: \(-7\times(-5) = 35\)

Answer:

\(\langle-42,35
angle\)