Question 346160: A) Find the inner product of a and b if a = <4, 5/4, -1/3> and b = < 1/2, -2, -3/2>, and state whether the vector are perpendicular.
a. 5; no
b. 5; yes
c. 0; yes
d. 0; no
B) Find the cross product of v and w if v = <-1/3, 4, -3/8> and w = < 6, -4/5, 4>
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Please, post one question at a time. I will answer part (a).
Let's compute the inner product, since that will maybe help with deciding which answer to pick.
a•b = 4(1/2) + (5/4)(-2) + (-1/3)(-3/2)
= 2 - 5/2 + 3/2
= 0
Then that narrows it down to (c) or (d).
Two vectors are perpendicular when their dot product is the cosine of 90 degrees, which is, as you may recall, 0.
Then (c) the correct answer.
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I decided to help you with question (b) as well.
Here we have
v = -i/3, 4j, -3k/8
w = 6i, -4j/5, 4k
v x w = (-i/3, 4j, -3k/8) x (6i, -4j/5, 4k)
v x w = 0 +4k/5 +4j/3 -24k +0 +16i -18j -12i/40 +0
v x w = (16 -12/40).i +(4/3 -18).j +(4/5 -24).k
v x w = 15.7(i) -50(j)/3 -116(k)/5 >================< ANSWER
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