Math 223
1.
2.
a.
Vector (cross) product
Name_____________________
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Let || a || 8, || b || 5 and
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a  b  30 . Find || a  b ||.
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Let v  2i  3 j  k and w  i  2 j .
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Find v  w
b. Find
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|| v  w ||
c. Show that
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v  w is perpendicular to both v and w .
d. Find the area of the parallelogram built on vectors
3.
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Find i  j   i  j .
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v and w .
4. Find a unit vector that is perpendicular to both
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d i k .
5. Let
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c i  j
and
A(2,  2,1), B3,  1, 2, C 3,  1,1, D4,  3, 4 .
a. Find the area of the triangle determined by the points
A, B, C.
b. Find the volume of the parallelepiped determined by A,
B, C, D.
c. Find a vector that is perpendicular to the plane containing points A,
and
C.
d. Find the distance from the point D to the plane containing points A,
and
B,
C.
B,