Question

Let u= (5, -12) and c= -3. What is || cu ||?
A- -39
B- 39
C- 21
D- 51

Answer 1

The norm of a point in the cartesian coordinate (x, y) is given by

`\mleft\Vert(x,y\mright)\mleft\Vert=\sqrt[]{x^2+y^2}\mright?`

For points c(x, y), the points will be (cx, cy), hence

`\mleft\Vert(cx,cy\mright)\mleft\Vert=\sqrt[]{(cx)^2+(cy)^2}\mright?`

From the question, we have

u = (5, -12)

c = -3

Therefore,

`\begin{gathered} cu=-3(5,-12) \\ =(-3*5,-3*-12) \\ cu=(-15,36) \end{gathered}`

||cu|| is given by

`\begin{gathered} \mleft\Vert cu\mleft\Vert=\sqrt[]{(-15)^2+36^2^{}}\mright?\mright? \\ =\sqrt[]{225+1296} \\ =\sqrt[]{1521} \\ \mleft\Vert cu\mleft\Vert=\mright?\mright?39 \end{gathered}`

Therefore, ||cu|| equals 39.

OPTION B is correct.