11.3, 11.4

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Author:
NateGatsby
ID:
196693
Filename:
11.3, 11.4
Updated:
2013-01-30 17:21:43
Tags:
calc1
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calc1
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  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.

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