Question

Find the vector v with the given magnitude and the same direction as u. magnitude direction v = 28 u = 0, 4, 4

Answer 1

The vector v with magnitude 28 and direction same as u = (0, 22.64, 22.64)

Given,

|| v || = 28

u = (0, 4, 4)

Here given that v has same direction as u, it must be a multiple n of u.

Then we have to find n:

For that,

$\sqrt{0n^{2}+4n^{2} +4n^{2} }$ = 28

$0n^{2}$ + $16n^{2}$ + $16n^{2}$ = $28^{2}$

$32n^{2}$ = 784

$n^{2}$ = 784 / 32

$n^{2}$ = 24.5

$n$ = $\sqrt{24.5}$

$n$ = 5.66

Therefore, the vector with magnitude 28 and direction same as u is,

v = (0 × 5.66, 4 × 5.66, 4 × 5.66)

v = (0, 22.64, 22.64)

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