You are looking down at a map. A vector with (length of vector u)= 8 points north and a vector with (length of vector v) = 8 points northeast.   The crossproduct (vector u) x (vector v) points:...

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You are looking down at a map. A vector with (length of vector u)= 8 points north and a vector with (length of vector v) = 8 points northeast.

 

The crossproduct (vector u) x (vector v) points:

A) south
B) northwest
C) up
D) down

What is the length of (vector u cross product vector v)

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The cross product of two vectors `u times v` is a vector at right angles to the other two vectors and obeys the right-hand-rule, which has you put your fingers of your right hand in the direction of the first vector (u) and curl in the direction of the second vector (v).  Your thumb then points in the direction of the cross product.

The fingers then point north, and need to curl east.  This means that your thumb is pointing into the page, which is part (d) down.

Also, the length of the cross product is given by 

`|u||v|sin 45=(8)(8)1/sqrt2=64{sqrt2}/2=32sqrt2`

The cross product has length `32sqrt2` and is pointing down into the page.

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