An auto mechanic knows the average time it takes to replace a defective car radiator is 70 minutes with a standard deviation of
1 answer:
You might be interested in
Answer:
a and b are perpendicular to each other, as are b and d, b and g
Step-by-step explanation:
To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.
We can find the angle between to vectors a and b from the following relation:
The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.
So
cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.
Now, for your exercise, let's compute the dot product between these vectors.
-----------
a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0
So a and b are perpendicular to each other.
------------
a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5
a and c are not perpendicular to each other.
--------------
a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7
So not perpendicular
---------------
a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11
Not
-----------------
b.c = (1,1,4).(1,3,1) = 1+3+4 = 8
Not
------------------
b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0
b.d = 0, so b and d are perpendicular to each other
--------------------
b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0
b.g = 0, perpendicular
---------------------
c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9
No
-----------------------
c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5
No
------------------------
d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7
No