P3 Vectors Watch

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Aristotle
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#1
Report Thread starter 13 years ago
#1
1) Given that u=3i+2j and [email protected], determine the value of @ such that:

a) u and v are at right angles.

b) u and v are parallel.

c) the acute angle between u and v is pi/4.

2) Find the angle, in degrees to 1 decimal place, which the vector a makes with the positive (i) x-axis (ii) y-axis (iii) z-axis, where a 5i+2j+4k.

Answers:

1a) -3.
1b) 4/3.
1c) 10.

2i) 41.8 degrees.
ii) 72.7 degrees.
iii) 53.4 degrees.

Cheers
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Feria
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#2
Report 13 years ago
#2
1. u=3i+2j [email protected]

a) uv=0 => [email protected]=0 => [email protected]=-6 => @=-3

b) uv=|u||v| => [email protected]=RT(9+4)RT([email protected]^2) => [email protected]=RT([email protected]^2)
([email protected])^[email protected]^2
[email protected][email protected]^[email protected]^2
[email protected]^[email protected]+16=0
([email protected])([email protected]) = 0 @=4/3

c) u.v=|u||v|Cos pi/4 => [email protected]=RT([email protected]^2)/RT(2)

2 ([email protected][email protected]^2)[email protected]^2
[email protected][email protected]^[email protected]^2
[email protected]^[email protected]=0 @=0.4 or @=10

2. Do the same thing, using u.v=|u||v|[email protected] where in each case, x axis = i, y axis = j and z axis = k. Substitute the values in like about and the angle between them @ will fall out nicely
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Aristotle
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#3
Report Thread starter 13 years ago
#3
(Original post by Feria)
2. Do the same thing, using u.v=|u||v|[email protected] where in each case, x axis = i, y axis = j and z axis = k. Substitute the values in like about and the angle between them @ will fall out nicely
Could you attempt oone of these questions and show the working out, because I'm struggling to apply what you are saying.

Thanks again
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