Hello all, not sure if this is the right thread but i need to check some of my answers to some problems. thanks.
if u = i + 2j - k and v = j - 3k are vectors in R^3. Find:
a) a unit vector poiting in the direction of -3u:
my solution: -3 (i + 2j - k) = -3i - 6j +3k
so then the magnitude is: root (9 +36 + 9) which is root (54) so then the unit vector is 1 / root(54) * (3i + 6j - 3k)
b) u * (12v)
i used the fact that u * (12v) is equal to 12 (u * v)
i first found u * v using the dot product formula to get 5. so then 12 (5) = 70.
c) the cosine of the angle between u and v.
I used the product i found earlier (5) and used the formula cos theta = u * v / (absolute value of u * absolute value of v) and got the answer 5 / root (60)
Now mind you, it may be just the way I am reading the question.
"a) a unit vector pointing in the direction of -3u"
The word 'pointing in the direction as means in the opposite direction as . That is the effect of the negative.
Positive multiples of are in the same direction, negative multiples are in the opposite direction
You answer above is a positive multiple.
If then is a unit vector parallel to in the same direction.
That is all part a) is asking for. You did a lot of unnecessary steps.