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

Answer:

The magnitude or size of the vector  ${\displaystyle {\overrightarrow {PQ}}}$ is:  $\sqrt{165}$

Step-by-step 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)

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

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

$\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}$

${\displaystyle {\overrightarrow {PQ}}}$ $=\sqrt{1^2+10^2+8^2}$

      $=\sqrt{1+100+64}$

      $=\sqrt{165}$

Therefore, the magnitude or size of the vector  ${\displaystyle {\overrightarrow {PQ}}}$ is:  $\sqrt{165}$