Question

If A = 6 i -8 j and B = - 16 i + 5 j , what is the magnitude of the vector C = 2 A - B ?

Answer 1

Choice a.
`35`

Explanation:

Note that
`i=(1,0)` and
`j=(0,1)`, so

`C=2A-B=2(6i-8j)-(-16i+5j)=12i-16j+16i-5j=28i-21j=(28,-21)`

Now the magnitude of a vector
`(x,y)` is
`√(x^2+y^2)`, thus the magnitude of
`C` is

`√(28^2+(-21)^2)=√(784+441)=√(1225)=35`