Question 1
Question
Select the expressions which are meaningful. Do not select the expressions which are meaningless and incorrect.
Answer
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(a dot b) dot c
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|a|(b dot c)
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a*b + c
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(a*b)c
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a*(b+c)
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|a|dot(b+c)
Question 2
Question
a dot b of <4,1, 1/4> and <6,-3,-8> is 19.
Question 3
Question
a dot b of: a=2i+j, b=i-j+k is 2.
Question 4
Question
Find the angle between the vectors. a = <3,-1,5>, b=<-2,4,3>. Ans: [blank_start]81[blank_end] degrees
Question 5
Question
Find the three angles of the triangle with the given vertices.
P(2,0), Q(0,3), R(3,4)
Ans:
p= [blank_start]48[blank_end] degrees
q= [blank_start]75[blank_end] degrees
r= [blank_start]57[blank_end] degrees
Question 6
Question
Determine whether the vectors are orthogonal, parallel, or neither.
a=<-5,3,7> , b=<6,-8,2>
Answer
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Orthogonal
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Parallel
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Neither
Question 7
Question
Determine whether the vectors are orthogonal, parallel, or neither.
a = <4,6>, b=<-3,2>
Answer
-
Orthogonal
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Parallel
-
Neither
Question 8
Question
Find the angles between the curves at their points of intersection.
y=x^2
y=x^3
ans: [blank_start]7/(5(sqrt2))[blank_end]
Question 9
Question
Find the scalar and vector projections of b onto a.
a=<3,6,-2>, b=<1,2,3>
ans:
comp_a(b)= [blank_start]9/7[blank_end]
proj_a(b) = <[blank_start]27/49, 54,49, -18/49[blank_end]>