Question

Let P = (2, 3, 4) and Q = (6, 1, 0). Find
(a) components for a vector of length 21 that points in the same direction as PQ
(b) coordinates for the point on segment PQ that is 1 unit from Q.

Answer 1

\(\vec{PQ} = \vec {PO} + \vec {OQ}\)

\(\vec{PQ} = -\vec {OP} + \vec {OQ} = \vec {OQ} -\vec {OP} \)

\(\vec{PQ} = <6,1,0> -<2,3,4> = <4,-2,-4>\)

now the length of \(\vec{PQ} \), ie it's magnitude, is : \(|\vec{PQ} | = \sqrt{ (4)^2 + (-2)^2 + (-4)^2 } = \sqrt{36} = 6\)

so the **unit vector** that points in that direction, ie \(\vec {PQ}\), and it has length 1 unit, and is \( \hat{PQ} = \dfrac{1}{6} <4,-2,-4> \)

will stop there Preetha as don't wanna break the rules :)