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- Thread starter masterofthewave124
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Hootenanny

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masterofthewave124 said:

I would express your answer in terms of unit vectors. Ordered pair notation is uaually used to define co-ordinates. Remember parallel vectors must be multipuls of each other.

~H

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let u be the vector.

the magnitude of 3i + 4j is 5

27/5 = 5.4

since parallel vectors are multiples of each other, we can just multiply (3i + 4j) by the scalar 5.4

so u = 5.4(3i + 4j)

= 16.2i + 21.6j

this is what i came up with before but it seems messy (decimals) and and kind of an inefficient solution

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arildno

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[tex]u=\frac{27}{5}(3i+4j)[/tex]

Note that [itex]\frac{1}{5}(3i+4j)[/itex] is a UNIT vector.

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looks much better. thanks!

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Hootenanny

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arildno said:Note that [itex]\frac{1}{5}(3i+4j)[/itex] is a UNIT vector.

Who said it wasn't a unit vector?

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arildno

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Noone. I just wanted to emphasize that, so that OP could see how a unit vector naturally would occur in his expression.Hootenanny said:Who said it wasn't a unit vector?

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Hootenanny

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arildno said:Noone. I just wanted to emphasize that, so that OP could see how a unit vector naturally would occur in his expression.

Ahh right, I thought I'd made a mistake somewhere .

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arildno

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is, indeed, the most natural one."I would express your answer in terms of unit vectors."

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Hootenanny

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arildno said:No, but I wanted OP to see why your suggestion

is, indeed, the most natural one.

Good point, I should have emphisised (but I didn't get the chance )

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state whether the following expressions are vectors, scalars or meaningless:

a) (a+b) • (a+c)

b) (a • a)b

c) (a • b)• c(b × c)

note that all the letters are vectors (so picture arrows on top of them)

mostly i need to clairify some things. first, whats the difference between a scalar and something meaningless? also for b) and c), what does something like (a • a)b compute to. does the b multiply, or dot, or cross or what?

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arildno

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to restate my other question, what does the b part of (a • a)b compute to. does the b multiply, or dot, or cross or what?

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arildno

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1. Dot product: Takes two vectors and produces a scalar.

2. Cross product: Takes two vectors and produces a vector.

3. Scalar multiplication: Takes a scalar and a vector, produces a vector that is parallell to the original vector.

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arildno

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What does a parenthesis usually signify for the order of operations performed?

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arildno

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What do YOU think?

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arildno

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Either way you are looking upon the last one, either as:

[tex]((a\cdot{b})\cdot{c})(b\times{c})[/tex]

or as:

[tex](a\cdot{b})\cdot({c}(b\times{c}))[/tex]

the expressions are meaningless.

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masterofthewave124 said:

(a • a) would result in a scalar value

hence that scalar result would then have to be multiplied with the vector b (scalar multiplication)

The final answer is a vector

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A parallelogram PQRS has vertices P(1, 3, 1), Q(4, 5, −2), S(−2, 3, −5). Determine

a) the coordinates of R

b) the perimeter of the parallelogram

c) the area of the parallelogram

if it was in 2-d if would be so much better but this is so hard to visualize!!

for a) i know i have to come up with an equation like PQ = RS, but then what do i do from there. do i add P and Q (R and S), subtract or what?

- #23

Hootenanny

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You must first find the vector equation of the line PQ.

~H

~H

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You can also approach the problem non vectorially .

What is the property of the point of intersection of diagonals of a parallelogram ?

For the area bit, I'd say vectors are cool .

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arunbg: what order are you talking about?

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