# 11.3, 11.4

The flashcards below were created by user NateGatsby on FreezingBlue Flashcards.

1. u = 2i + j − 4k
v = i − 6j + 3k

Find:
u · v
u · u
||u||2
(u · v)v
u · (2v)
• -16
• 21
• 21
• -16i + 96j - 48k
• -32
2. Determine whether u and v are orthogonal, parallel, or neither.

u = −9i + 80j − k
v = 9i + j − k
orthogonal
3. Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines is 1.
u = i + 2j + 2k
• 1/3
• 2/3
• 2/3
4. Find the direction angles of the vector.

u = < 3, 2, −3 >
•  = 50.2 degrees
•  = 64.8
•  = 129.8
5. u = < −9, −5, −6 >
v = < 4, 1, −3 >

u · v
u · u
||u||2
(u · v)v
u · (2v).
• -23
• 142
• 142
• -92i - 23j + 69k
• -46
6. The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle.

(-9, 0, 0)
(0, 0, 0)
(1, 2, 9)
obtuse
7. The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle.

(-5, 0, 0)
(0, 0, 0)
(4, 8, 3)
obtuse
8. Find two vectors in opposite directions that are orthogonal to the vector u.

u = − 54i + 92j
• 4i/5 + 2j/9
• -4i/5 - 2j/9
9. Find the angle between a cube's diagonal and one of its edges.
54.7 degrees
10. u = 6i + 6k
v = 6i + 7j − 5k.

Find:
u × v
v × u
v × v
• -42i + 66j + 42k
• 42i - 66j - 42k
• 0
11. u = <20, -5, 0 >
v = <-2, 5, 0 >

Find:
u x v

Is u x v orthogonal to u or v?
4k

It's orthogonal to both.
12. u = -4, 0, 10
v = 3, -1, 0

Find u x v.

Is u x v orthogonal to u and v?
<10,30,4>

It's orthogonal to both.
13. u = i + j + k
v = 2i + j − k

find u x v.

Is u x v orthogonal to u or v?
<-2,3,-1>

It's orthogonal to both.
14. Find u · (v × w).

u = <8, 0, 0>
v = <5, 5, 5>
w = <0, 8, 8 >
0
15. Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w.

u = i + j
v = j + k
w = i + k
2 units3
16. u = -2, 1, 5
v = 0, 4, 0

Find u x v.

Is u x v orthogonal to u and v?
<-20,0,-8>

It's orthogonal to both.
 Author: NateGatsby ID: 196693 Card Set: 11.3, 11.4 Updated: 2013-01-30 22:21:43 Tags: calc1 Folders: Description: calc1 Show Answers: