Question
Find any vector w that is perpendicular to both vector "u = 3j + 4k" and vector "v = 2i".
Note: i, j and k are unit vectors
How would you solve this problem? Please walk me through?
Note: i, j and k are unit vectors
How would you solve this problem? Please walk me through?
Answers
Reiny
Two vectors are perpendicular if their dot product is zero
so you want a vector w = (a,b,c) so that
(a,b,c)∙(0,3,4) = 0 and
(a,b,c)∙(2,0,0) = 0
from the second 2a = 0, so a=0
from the first 3b+4c=0
or 3b=-4c
b/c = -4/3, if we let c=3 and b=-4 that would work
Notice there is more than one solution
as long as our vector w has direction (0,-4,3)
so you want a vector w = (a,b,c) so that
(a,b,c)∙(0,3,4) = 0 and
(a,b,c)∙(2,0,0) = 0
from the second 2a = 0, so a=0
from the first 3b+4c=0
or 3b=-4c
b/c = -4/3, if we let c=3 and b=-4 that would work
Notice there is more than one solution
as long as our vector w has direction (0,-4,3)