Question

If vector u = [1,-3,-2] and vector v = [4,-5,3] find:




a) |vector u + vector v - 5j |




b) Find Q, where P (-7,5,-1] and vector PQ=2(vector u)





c)find vector w which is orthogonal to both vector u and vector v

Answer 1

if you are using the standard notiation to label a vector with [i, j, k]
then 5j would be [0, 5, 0]

a) |vector u + vector v - 5j |
= |[1,-3,-2] + [4,-5,3] - [0,5,0] |
= | [5, -13, 1]
= √(25+169+1)
= √195

b) let Q be (x,y,z)
then PQ = [x+7,y-5,z+1]
but PQ = 2u = [2,-6,-4]

then:
x+7=2 --->x = -5
y-5=-6 --->y = -1
z+1 = -4 --> z = -5

Q is (-5,-1,-5)

c) you want u x u, the cross-product
I don't know what method you have learned, but you must have one.
See if you can come up with [19,11,-7]

Answer 2

thanks! Does, vector u x vector v = vector w?