vectors, find v, a, s

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September 8th 2009, 08:03 PM
Arez

vectors, find v, a, s

Quote:

If both u X v = 0 and u.v = 0, what can you conclude about u or v

i don't know what theyre getting at

Quote:

Find velocity v, acceleration a, and speed s at the indicated time t = t1 for r(t) = sin2ti + cos3tj + cos4tk; t1 = pi / 2

im not sure where to start here, please help
September 8th 2009, 08:13 PM
seld

well u x v = 0

you know |u x v | = |u||v|sin(b)

b being the angle between the 2 vectors.

So that means that b has to be 0 or 180 degrees.

you know that u * v = |u||v|cos(c)

where c is the angle between the 2 vectors.

So if the dot product is equal to zero, then it means that the angle between the 2 vectors is 90 or 270.

can you take it from there?

then the second question you have

v(t) is the first derivative of r(t), and a(t) is the second derivative of r(t)
September 8th 2009, 08:51 PM
Amer

Quote:

Originally Posted by Arez

i don't know what theyre getting at

im not sure where to start here, please help

it can be exist in the space two vector orthogonal and parallel to each other at the same time ??

since if $v\times u =0$ we said that the two vectors are parallel and if $v\cdot u = 0$ the two vectors are orthogonal

that can't be happened since if two vector are orthogonal they will intersect and they are parallel they will not intersect contradiction

the second question

$velocity = r'(t)$

$acceleration = r''(t) = v'(t)$

$speed=\parallel v \parallel$

$r(t) = \sin 2t i + \cos 3t j + \cos 4t k$

$v(t)= 2\cos 2t i -3 \sin 3t j - 4\sin 4t k$

$a(t) = -4\sin 2t i -9\cos 3t \hat{j} -16\cos 4t k$

$s = \parallel v \parallel = \sqrt{(2\cos 2t )^2 + (-3\sin 3t)^2 + (-4\sin 4t)^2 }$