find vector of magnitude 3 in direction of v = 18i - 24k?

first you need to find the unit vector, which is in itself a pure direction. 1/1=1, 5/5=1, 10000/10000=1

so as long as we divide the numerator be the denominator, we get the same vector w/ a mag of 1. We can then multiply anything by that vector and have the magnitude be what me multiplied it by. ie, 1*5= 5, 1*3=3 etc.

so to find the mag of v, it is just like finding the hyp of a triangle. sqrt((18)^2+(-24)^2) = 30. So if we divide each component by the overall magnitude, we get a ratio of how much each unit direction (i, j,k) weights in to the resultant direction, or the direction of v.

so 18/30(i) -24/30(k) is the pure direction of that vector. if we were to find the mag of that, sqrt((18/30)^2+(-24/30)^2) = 1. but because we kept the ratio of each component in tact, we have the same direction of v.

we can then multiply the unit vector by 3 and get the final answer. 3*(18/30)i -(3*-24/30)k = 18/10i - 24/10k. if you take the mag of that, you will get 3 because we just multiplied 3*1.

another thing to note in these problems. |18/30|<1, |-24/30|<1. If we had 30/30=1, then it would be the only component, and thus the only vector. Ie, if v=30i, then the unit vector would just be in the i direction. if we had v = i+j, then the hyp between the two would be greater than 1, and it wouldn't be a unit vector. Basically, after you find the unit vector, the mag of each component needs to be less than 1, or equal to 1 if there is only 1 component. It can NEVER be >1.

assume you're talking approximately 3 dimensions i, j,ok The vector could have the form |a| (10, 0, -24 ) |a| sqrt ( 10^2 +0^ 2 + (-24)^2 ) = |a| sqrt(676) =3 fixing a = 3/26 or -3/26 hence the vector would be 3/26( 10i -24k) or ( -3/26) (10i - 24k )

maybe someday will make use of this answer.. it's 9/5, 0 , -12/5