Vector Calc Homework: Find Unit Vector in Direction of ⃗rP & P to Q

[~Sam~]

Homework Statement

1. Consider the point P at position ⃗rP = (−3.0 mm)ˆı + (4.0 mm)jˆ. Give an expression for rˆP , the unit vector in the direction of ⃗r.

2. Consider the point P from exercise 1 and another point Q at position ⃗rQ = (8.0 mm)jˆ. Give an expression for rˆPQ, the unit vector in the direction from P to Q.

Homework Equations

Not much really..maybe length formula

The Attempt at a Solution

I was wondering...x/sqrt(x^2+y^2) i +y/sqrt(x^2+y^2) plug it into get (3/5)i+(4/5)j

For part two..would I subtract rQ-rP...so 4.0j-[-3.0i+4.0j)? Or would it be 4.0j-[(3/5)i+(4/5)j)? Then do the same..x/sqrt(x^2+y^2) i +y/sqrt(x^2+y^2)?

 

[Mark44]

Homework Statement

1. Consider the point P at position ⃗rP = (−3.0 mm)ˆı + (4.0 mm)jˆ. Give an expression for rˆP , the unit vector in the direction of ⃗r.

2. Consider the point P from exercise 1 and another point Q at position ⃗rQ = (8.0 mm)jˆ. Give an expression for rˆPQ, the unit vector in the direction from P to Q.

Homework Equations

Not much really..maybe length formula

The Attempt at a Solution

I was wondering...x/sqrt(x^2+y^2) i +y/sqrt(x^2+y^2) plug it into get (3/5)i+(4/5)j

For part two..would I subtract rQ-rP...so 4.0j-[-3.0i+4.0j)? Or would it be 4.0j-[(3/5)i+(4/5)j)? Then do the same..x/sqrt(x^2+y^2) i +y/sqrt(x^2+y^2)?

There are a lot of characters in what you wrote that aren't rendering correctly, so I'm not 100% sure of what you wrote.

One relevant equation that you didn't think to add is the one for the magnitude of a vector. If v = ai + bj + ck = <a, b, c> is a nonzero vector, then a unit vector with the same direction as v is (1/|v|)v = (1/sqrt(a² + b² + c²))<a, b, c>.