Find the angle between the given vectors . Round to the nearest tenth of a degree. 1) u= -3i +6j ,v=5i + 2j 2) u= i -j , v=2i +3j Use the dot product

CMIIh

CMIIh

Answered question

2021-06-02

Find the angle between the given vectors . Round to the nearest tenth of a degree.
1) u= -3i +6j ,v=5i + 2j
2) u= i -j , v=2i +3j
Use the dot product to determiine wheter the vectors are parallel, orthogonal , or neither .
1) v = 2i +j, w = i-2j
2) v = 4i-j , w=8i-2j
3) v= 3i +3j , w=3i -2j
Find proj w v
1) v = 2i +3j . w = 8i- 6j
2) v= 2i -3j . w =-3i +j

Answer & Explanation

smallq9

smallq9

Skilled2021-06-03Added 106 answers

I have solved your question. Here are the explanations.

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Jeffrey Jordon

Jeffrey Jordon

Expert2021-09-08Added 2605 answers

1) 4=3i+6j; v=5i+2j

cosθ=uv|u||v|=(3i+6j)(5i+2j)|(3i+6j)||(5i+2j)|

cosθ=15+129+3625+4=33529=1145

θ=cos1(1145)=πcos1(1145)=1808863

θ=91.372

2) v=2i+j, w=iej

vw=(2i+j)(i2j)=22=0

vw=0 V and w are orthogonal

3) projwv=wvvvv

projwv=(2i+3j)(8i6j)(2i+3j)(2i+3j)(2i+3j)

=16184+9(2i+3j)=213(2i+13j)

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