Vector5.13

Question

Find a unit vector in the direction of the vector v=⟨√2,√2⟩.

 

Please show step by step work to solution and provide final answer. Please and Thank You!

Answer 1

The vector's x component is √2.  The y component is √2.

 

To find the magnitude of the vector, we use the Pythagorean theorm.

 

Magnitude = √(√(2)² + (√2)²)

                = √(2 + 2)

                = 2

 

To find the direction, take the inverse tangent of √2 / √2.  That would be 45 degrees because the x and y components are the same value.

 

 

v = 2(cos45i + sin45j)