Question

determine the size of PQ where the position vectors of points P and Q are 2i- 3j + 4k and 3i -7j +12k respectively​

Answer 1

The magnitude or size of the vector
`{\displaystyle {\overrightarrow {PQ}}}` is:
`√(165)`

Explanation:

As the position vectors of points P and Q are
`2i- 3j + 4k` and
`3i -7j +12k`

So the given vectors

• P(2, -3, 4)

• Q(3, -7, 12)

`{\displaystyle {\overrightarrow {PQ}}}=(3-2)i+(-7-(-3)j+(12-4)k`

`{\displaystyle {\overrightarrow {PQ}}}=i+10j+8k`

`\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrtx_i\right`

`{\displaystyle {\overrightarrow {PQ}}}`
`=√(1^2+10^2+8^2)`

`=√(1+100+64)`

`=√(165)`

Therefore, the magnitude or size of the vector
`{\displaystyle {\overrightarrow {PQ}}}` is:
`√(165)`