Question

In a cartesian co-ordinate system the coordinate of two points p and q are (2,4,4) and (-2, - 3,7) respectively. Find pq and its magnitude

Answer 1

The answer to the question is (-4,-7,3) and $\sqrt{74}$

CALCULATION:

The coordinates of the two points p and q is given as (2,4,4) and (-2,-3,7) respectively.

The position vector of point p is $2\hat i+4\hat j+4\hat k$

The position vector of point q is $-2\hat i-3\hat j+7\hat k$

We are asked to calculate pq.

Hence, $\vec pq\ =\ \vec q-\vec p$

                            = $(-2\hat i-3\hat j+7\hat k)-(2\hat i+2\hat j+4\hat k)$

                            = $(-2-2)\hat i+(-3-4)\hat j+(7-4)\hat k$

                            = $-4\hat i-7\hat j+3\hat k$

The magnitude of pq is calculated as -

                               $pq\ =\ \sqrt{(-4)^2+(-7)^2+3^2}$

                                      $=\sqrt{16+49+9}$

                                      $=\sqrt{74}$        [ans]

Answer 2

That's your answer....

Hope this will help you??!!✌️✌️