I need help with my vectors unit. I'm really confused about how to set them up. Please help.
a.) Given u=2i-5j and v=-i+3j, determine -6u-3v?
b.) Find the component form of v if |v|=4 and the angle it makes with the x-axis is 60 degree.
c.) Given u=5i+3j and v+3i+2j, find (u)(v).
d.) Find the angle between the vectors u and v if u=-4i+2j and v=3i+2j.
2 answers
UPDATE: I figured it out.
-6u-3v = -6(2i-5j) - 3(-i+3j)
= -12i+30j+3i-9j
= -9i+21j
|-6u-3v| = √(81+441) = √522
x = |v| cosθ and y = |v| sinθ
Since cos60° = 1/2 and sin60° = √3/2
v = (4(1/2),4(√3/2)) = (2,2√3)
I assume that (u)(v) means u•v
If so, then
u•v = (5i+3j)•(3i+2j) = 5*3 + 3*2 = 21
Since u•v = |u|*|v| cosθ, we have
-12 + 4 = √20 * √13 cosθ
cosθ = -8/√260
θ = 119.74°
= -12i+30j+3i-9j
= -9i+21j
|-6u-3v| = √(81+441) = √522
x = |v| cosθ and y = |v| sinθ
Since cos60° = 1/2 and sin60° = √3/2
v = (4(1/2),4(√3/2)) = (2,2√3)
I assume that (u)(v) means u•v
If so, then
u•v = (5i+3j)•(3i+2j) = 5*3 + 3*2 = 21
Since u•v = |u|*|v| cosθ, we have
-12 + 4 = √20 * √13 cosθ
cosθ = -8/√260
θ = 119.74°
3 answers