Points P and Q are located at (0, 2, 4) and (-3, 1,5). Calculate a) The position vector of P

b) The distance vector from P to Q

c) The distance between P and Q

d) A vector parallel to PQ with magnitude of 10

a) The position vector of P is .

b) The distance vector from P to Q is .

c) The distance between P and Q is .

d) A vector parallel to PQ with magnitude of 10 is .

Explanation:

a) The position vector of a point is the vector displacement from the origin to the location of the point. That is:

The position vector of P is .

b) First, we calculate the position vector of point Q:

The distance vector from P to Q is define by the following vectorial expression:

(1)

The distance vector from P to Q is .

c) There are two approaches to calculate the distance between P and Q:

First Method - Pythagorean Theorem:

Second Method - Dot Product:

(2)

The distance between P and Q is .

d) To determine a vector parallel to PQ with a given magnitude is determined by the following expression:

(3)

Where is the scale factor.

If we know that , and , then the vector is:

A vector parallel to PQ with magnitude of 10 is .

it was given as a lesson and guide for prayer.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach