Question

question
given vector ( mathbf{v}=langle 6,4
angle ), find ( -0.5 mathbf{v} ) graphically by stretching the vector by its tip and then writing
the result in component form.

Explanation:

Step1: Multiply each component by -0.5

Given \(\mathbf{v}=\langle6,4
angle\), to find \(-0.5\mathbf{v}\), we use the scalar - vector multiplication rule \(\text{If }\mathbf{v}=\langle a,b
angle\text{ and }k\text{ is a scalar, then }k\mathbf{v}=\langle ka,kb
angle\).
For the \(x\) - component: \(k\times a=-0.5\times6\)
For the \(y\) - component: \(k\times b=-0.5\times4\)

Step2: Calculate the new components

\(-0.5\times6=-3\)
\(-0.5\times4 = - 2\)

Answer:

\(\langle-3,-2
angle\)