Question

15 points!!!Let v = (2,8) and w = (-1,-4). Which of the following is true? Check all thatapply.A. v and w are perpendicular B. The x-component of v is 2C. v= -2wD. v+w= -34

Answer 1

$\begin{gathered} v=(2,8) \\ w=(-1,-4) \end{gathered}$

A. v and w are perpendicular ?

Let's do the perpendicular test:

$\begin{gathered} If \\ v\cdot w=0,then \\ v\perp w \end{gathered}$$\begin{gathered} v\cdot w=v1w1+v2w2+\cdots v_nw_n \\ w\cdot w=2(-1)+8(-4)=-2+(-32)=-32 \\ -32\ne0 \end{gathered}$

Therefore v and w are not perpendicular

B. The x-component of v is 2:

$\begin{gathered} v=(x,y)=(2,8) \\ x=2 \\ y=8 \end{gathered}$

This is true

C. v = -2w

$\begin{gathered} v=(2,8) \\ w=(-1,-4) \\ 2w=(-2\times(-1),-2\times(-4)) \\ 2w=(2,8)=(2,8) \\ v=-2w \end{gathered}$

This is true

D.

$\begin{gathered} v+w=(v1+w1,v2+w2,\ldots+,v_n+w_n) \\ v+w=(2+(-1),8+(-4)) \\ v+w=(1,4) \\ \parallel v+w\parallel=\sqrt[]{1^2+4^2}=\sqrt[]{17}\ne-34 \end{gathered}$

This is false