U=sqrt{5i}-8j, V=5i,j. Find the angle between the Vectors

Question

I really need these solved

Answer 1

Recall that the formula for the angle θ between two vectors in U,V ∈ Rⁿ is cos θ = (U·V)/(||U||*||V||)

 

You probably made a typo when writing what V is.

 

For U = ⟨√5,-8⟩ and V = ⟨5,1⟩, we have

 

U·V = -8+5√5

||U|| = √(5+64) = √69

||V|| = √(25+1) = √26

θ = cos^-1 (-8+5√5)/√[(69)(26)] ≈ 85.69°

 

 

For U = ⟨√5,-8⟩ and V = ⟨5,-1⟩, we have

U·V = 8+5√5
||U|| = √(5+64) = √69
||V|| = √(25+1) = √26
θ = cos^-1 (8+5√5)/√[(69)(26)] ≈ 63.07°