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Calc 3 10.4

 

<== Calculus 3
Number Question Answer
See the work

1.

 

 

Find the cross product a x b where a= <1, 4, -1>
and b= <-2,5,2>.
a x b= < __,__,__>

 

a x b= < 13,0,13>

 

The work

2.

 

Let a=(4,7,4) and b=(5,10,5) be vectors.
Compute the cross product a x b= (__,__,__)

 

a x b= (-5,0,5)

 

The work

3.

 

 

Find the cross product c x d where c= 1i-5j-4k
and d= 1i- 3j-3k.
c x d= _____i+_____j+______k

 

c x d= 3i-1j+2k
The work

4.

 

 

 

 

 

You are looking down at a map. A vector u with
lul= 3 points north and a vector v with lvl= 2 points
northeast. The crossproduct u x v points:
A) south
B) northwest
C) up
D) down
Correct answer:___
The magnitude |u x v|=___

 

Correct answer:D
|u x v|=(6sqrt(2)/2)
The work

5.

 

 

 

Think of the letter X as four vectors starting from the center
and pointing outward. Label the four vectors starting from the
top left and proceeding clockwise as u, v, w, z.
Does u x v point in or out of the page? (in/out)____
Does u x z point in or out of the page? (in/out)____
Compute u x w= <___,___,___>

 

uv point: in
u x z point: out 
w= <0,0,0>

 

The work
6. If a = i+3j+k and b = i+7j+k, find a unit vector
with positive first coordinate orthogonal to both a and b.
____i + ______j + ______k
 0.707106781186547i
 0j
 -0.707106781186547k
The work
7. Find two unit vectors orthogonal to a = <3, 4, 1> and
b = < 1, 2, 4>
Enter your answer so that the first non-zero coordinate of the
first vector is positive.
First Vector: < _____ , _______ , ______>
Second Vector: < ______, ______, _____ >

 

First Vector:
< 0.7814038 , -0.61396013 , 0.11163>

Second Vector:
< -0.781404,  0.61396,  -0.11163>

The work
8. Find the area of the triangle with vertices:
Q(0,0,-5), R(-3,-3,-8), S(-6,-2,-10).
7.64852927038918
The work
9. Find the area of the parallelogram with vertices:
P(0,0,0), Q(-4,-4,5), R(-4,-3,3), S(-8,-7,8).
9.4339811320566
The work