Another Precal Vector question?

Question

Find the component of u along v if v = 7i and v = 8i+6j

Please help i need this in half an hour,

Answer 1

I assume you mean u = 7i.

If vectors u and v are separated by an angle θ, the projection of u on v is:

|| u || cosθ

The dot product of u and v is:
u • v = || u || || v || cos

|| u || cosθ = (u • v) / || v ||

The dot product of u and v is:
u • v = <7, 0> • <8, 6> = 56 + 0 = 56

The magnitude of v is:
|| v || = √(8² + 6²) = √(64 + 36) = √100 = 10

The projection of u on v is:

|| u || cosθ = (u • v) / || v || = 56/10 = 5.6

Answer 2

Draw a photograph. Use the vecors to form a triangle with legs of three and 5 km/hr. Draw the hypotenuse for their vector sum. Use pythagorean thm. Vector Sum magnitude= Sqrt(3^2+5^2)=5.8m/s