Finding Unit Vectors in Same Position

Question

For each different vector, find a unit vector in the same direction.

 

​a.​u1 = [ −5, 3]

​b.​u2 = ​with point M = (2, −8) and point N = (−5, 4).

​c.​u3 is the vector with magnitude 6 and direction angle of 225° .

Answer 1

A unit vector is a vector with a magnitude of 1. To turn any vector into a unit vector in the same direction involves finding the magnitude, then dividing each component of the vector by the magnitude.

a) u1=<-5,3> the magnitude = √[ (-5)²+(3)² ] = √ (25+9) = √34

so the unit vector in the same direction is < -5/√34, 3/√34 >

b) u2 = < 4-(-8) , (-5) - 2 > = <12, -7> the magnitude is √[ (12)²+(-7)² ] √(144+49) = √193

so the unit vector in the same direction as <12, -7> is

<12/√193, -7/√193 >

c) u3 is actually deceptively simple. They gave you the direction already, so the unit vector in the

same direction is a vector with magnitude of 1, and a direction angle of 225 degrees. If they

want this in x-y-component form, then we would need to compute: 1 ·cos225 = x-component and

1·sin225 = y-component or < -√2/2, -√2/2 >