Question

for the vector ( r=langle -5,-1
angle ), find ( -5r ). ( -5r=langlesquare,square
angle )

Explanation:

Step1: Recall scalar multiplication of vectors

To multiply a vector \(\mathbf{r}=\langle a,b
angle\) by a scalar \(k\), we use the rule \(k\mathbf{r}=\langle ka,kb
angle\). Here, \(\mathbf{r}=\langle -5,-1
angle\) and \(k = - 5\).

Step2: Multiply each component by -5

For the first component: \(-5\times(-5)=25\)
For the second component: \(-5\times(-1) = 5\)
So, \(-5\mathbf{r}=\langle25,5
angle\)

Answer:

\(\langle 25, 5
angle\)