Arturo O. answered • 03/26/17
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(a)
First, find the vector from A to B. Call it V. Then divide V by its magnitude, and that will be the unit vector u parallel to AB.
u = V / |V|
V = (Bx - Ax)i + (By - Ay)j + (Bz - Az)k = (-1 - 2)i + [0 - (-1)]j + (3 - 4)k
V = -3i + j - k
|V| = √[(-3)2 + (1)2 + (-1)2] = √11
u = V / |V| = (-3i + j - k) / √11
You can simplify it further from here.
(b)
Find a vector opposite to AB and of length 4, Call it R.
R = -4u,
where u is the unit vector from part (a). You should be able to finish from here.
Arturo O.
Mark,
In the problem statement for (b), we are asked to find a vector directed oppositely to AB, so we can take the unit vector pointing in the AB direction, multiply it by -1 to make it anti-parallel to AB, and multiply by the desired magnitude.
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03/26/17
Mark M.
03/26/17