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Find the components of the vector v with given point P and terminal point Q,

Asked Nov 8, 2009, 01:29 AM — 1 Answer

Find the components of the vector v with given point P and terminal point Q, find te unit vector in the direction of v.
1. P: (3.2.0) Q: (5, -2,0)

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galactus Posts: 2,272, Reputation: 1436

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Nov 8, 2009, 04:04 AM

Given vectors $P=<3,2,0>, \;\ Q=<5,-2,0>$

If $\overline{PQ}$ is a vector in 3-space with initial point $P(x_{1},y_{1},z_{1})$ and terminal $Q(x_{2},y_{2},z_{2})$ , then

$\overline{PQ}=<x_{2}-x_{1}, \;\ y_{2}-y_{1}, \;\ z_{2}-z_{1}>$

So, from the given vectors, we have $<5-3, \;\ -2-2, \;\ 0-0>=<2,-4,0>$

When we find a unit vector, we normalize.

Find the norm, which is just Pythagoras. A norm is a distance or length. The length of the vector.

$||PQ||=\sqrt{2^{2}+(-4)^{2}}=\sqrt{20}=4\sqrt{2}$

To normalize, we take the reciprocal and get $\frac{1}{4\sqrt{2}}=\frac{\sqrt{2}}{8}$

A unit vector is $\frac{1}{||v||}\cdot v=\frac{\sqrt{2}}{8}\cdot <2,4,0>$

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