Anonymous A. answered • 04/11/21
A pre-student teacher with a passion for math!
Hi Ivy,
(a) Yes! Looks like you've gotten vector magnitudes down :)
(b) When adding two vectors, you have to add corresponding components together (i with i, j with j, etc.). So if s= a+b, then you add vectors a and b component-wise. This looks something like
s = (2 + (-3))i + (4+0)j + ((-6)+1)k
s = -1i + 4j -5k
In component form, s = 〈-1,4,-5〉
(c) When multiplying vectors by a constant, you need to multiply each separate component by the constant. In this case,
m = -3b = -3(-3i + k)
m = 9i -3k
In component form, m =〈9,0,-3〉
(d) There's two steps to solving this one. First, we need to find vector d, and then we need to find its magnitude.
Similar to adding vectors, when you subtract vectors, you need to do it by component. Remember, order is important! This question defines vector d = c - b. So you need to subtract the components of vector b from the components of vector c, as such
d = (3j - 2k) - (-3i+k)
Be careful to subtract the right components. Note that vector c doesn't have an i component, and vector b doesn't have a j component. Sometimes it helps to rewrite your vectors using all 3 components. This would look like
d = (0i +3j -2k) - (-3i + 0j + k)
And now all we do is subtract component-wise.
d = (0 - (-3))i + (3-0)j + (-2-1)k
d = 3i + 3j -3k
Now you just have to find the magnitude of vector d. From part (a), it looks like you have this covered, but I'll go through the calculation anyway:
|d| = √((3)2+(3)2+(-3)2)
=√(27)
=3√(3)
Hope this helps!
Ivy K.
Yes it does! Tysm :)04/12/21