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Hey guys, I know I've left it kind of late, but I have a calc. unit test tomorrow at 10AM. I was doing the assigned review, and some extra questions of top of it, and these ones are still giving me trouble.

Any help at all you could offer would be greatly appreciated, as I have to pull my mark up back to an 80-82% (i'm sitting at a 77% right now, we just finished a tough unit)

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#3a. Find the dot product of the two vectors u and v where u=(3,-4,1) and v=(2,1,5)

b. Find the angle between u and v.

For this question, i copied part B from a friend, in hopes of understanding it, but I'm still not sure how to find the angle.

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#7. The cosine of the angle between a and b is 4/21. Find p, if a=6i+3j-2k and b=-2i+pj-4k

For this one, I'm not even sure if I'm on the right track. I think I just confused myself

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#9. Calculate the dot product of 4x-y and 2x+3y if |x|=3, |y|=4 and the angle between x and y is 60degrees.

I'm not sure where to go on this one either.

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#12. A triangle has vertices A(-1,3,4), B(3,-1,1) and C(5,1,1)

a) show that the triangle is right-angled

b) Calculate the area of the triangle

c) Calculate the perimeter of triangle ABS

d) Determine the forth vertex needed to complete a rectangle

Whenever I try to graph 3D shapes, I get confused. I have my drawing below, but I still can't visualize how it looks. Also how do I get the area of the triangle without the height?

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#13. Find the projection of u=(17,-3,8)

a) onto each of the coordinate axes

b) onto each of the coordinate planes

I remember doing the projection stuff, its applications of dot product if I'm not mistaken, but we never did an example like this, only ones projecting one given vector on another (both with numbers)

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#14. Use the cross product to find the area of the triangle whose vertices all lie in the xy-plane at coordinates A(-7,3,0), B(3,1,0), and C(2,-6,0)

No idea what to do here :(

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#1 What can you conclude about the vectors u and v if

c) u x v = 0

d) |u x v| = |u||v|

e) (u x v) dot u = 0

f) (u x v) x u = 0

These communication questions always get me, again I'm stumped.

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#2 Given u=6i+3j+2k and v=-3i+4j+k find

d) a unit vector perpendicular to both u and v

Where did I go wrong in my calculations here?

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#3a) Draw x-, y- and z-axes and make a sketch of

i) the position vector OP of the point P(3,-2,5)

ii) the projection of OP onto the z-axis

iii) the projection of OP onto the xy-plane

b) Determine the magnitudes of the projections in a, parts ii and iii.

This one is similar to #13, but like I said before, we've never done an example of a projection onto an axis or plane.

http://img399.imageshack.us/img399/6462/tehinterwebsjb5.jpg [Broken]

Any help at all you could offer would be greatly appreciated, as I have to pull my mark up back to an 80-82% (i'm sitting at a 77% right now, we just finished a tough unit)

**Homework Statement**----------

#3a. Find the dot product of the two vectors u and v where u=(3,-4,1) and v=(2,1,5)

b. Find the angle between u and v.

For this question, i copied part B from a friend, in hopes of understanding it, but I'm still not sure how to find the angle.

-----------

#7. The cosine of the angle between a and b is 4/21. Find p, if a=6i+3j-2k and b=-2i+pj-4k

For this one, I'm not even sure if I'm on the right track. I think I just confused myself

-----------

#9. Calculate the dot product of 4x-y and 2x+3y if |x|=3, |y|=4 and the angle between x and y is 60degrees.

I'm not sure where to go on this one either.

------------

#12. A triangle has vertices A(-1,3,4), B(3,-1,1) and C(5,1,1)

a) show that the triangle is right-angled

b) Calculate the area of the triangle

c) Calculate the perimeter of triangle ABS

d) Determine the forth vertex needed to complete a rectangle

Whenever I try to graph 3D shapes, I get confused. I have my drawing below, but I still can't visualize how it looks. Also how do I get the area of the triangle without the height?

------------

#13. Find the projection of u=(17,-3,8)

a) onto each of the coordinate axes

b) onto each of the coordinate planes

I remember doing the projection stuff, its applications of dot product if I'm not mistaken, but we never did an example like this, only ones projecting one given vector on another (both with numbers)

------------

#14. Use the cross product to find the area of the triangle whose vertices all lie in the xy-plane at coordinates A(-7,3,0), B(3,1,0), and C(2,-6,0)

No idea what to do here :(

-------------

#1 What can you conclude about the vectors u and v if

c) u x v = 0

d) |u x v| = |u||v|

e) (u x v) dot u = 0

f) (u x v) x u = 0

These communication questions always get me, again I'm stumped.

--------------

#2 Given u=6i+3j+2k and v=-3i+4j+k find

d) a unit vector perpendicular to both u and v

Where did I go wrong in my calculations here?

---------------

#3a) Draw x-, y- and z-axes and make a sketch of

i) the position vector OP of the point P(3,-2,5)

ii) the projection of OP onto the z-axis

iii) the projection of OP onto the xy-plane

b) Determine the magnitudes of the projections in a, parts ii and iii.

This one is similar to #13, but like I said before, we've never done an example of a projection onto an axis or plane.

**The attempt at a solution**http://img399.imageshack.us/img399/6462/tehinterwebsjb5.jpg [Broken]

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