Question #8893

a force of 20N is directed from (1,2,3) to (2,2,4). experss force as a vector in terms of unit coordinate vector.

Expert's answer

Let's find the vector V that is directed from P1 = (1,2,3) to P2 = (2,2,4):

V = P2 - P1 = (2-1,2-2,4-3) = (1,0,1).

Let's normalize this vector so it's be the unit lenght:

|V| = √(1² + 0² + 1²) = √2;

V = (1,0,1)/√2 (now |V|=1).

Now we can multiple this vector by 20N to get final force vector:

F = 20V = 20(1,0,1)/√2.

V = P2 - P1 = (2-1,2-2,4-3) = (1,0,1).

Let's normalize this vector so it's be the unit lenght:

|V| = √(1² + 0² + 1²) = √2;

V = (1,0,1)/√2 (now |V|=1).

Now we can multiple this vector by 20N to get final force vector:

F = 20V = 20(1,0,1)/√2.

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