|u| = 4, |v| = 4, and the angle between u and v (when placed tail to tail) is 90 degrees. Find |u| - |v|
a) -1
b) 5
c) 25
d) 12
We know
u dot v = |u| |v| cos θ , where θ = 90°
u dot v = (4)(4)cos90 = 0
of course we already know that the dot product between perpendicular
vectors is 0
Your question is:
find |u| - |v| , but since you said: |u| = 4, |v| = 4
= 4-4
= 0
am I missing something here?
oh sorry i meant that |u| = 3, |v| = 4
To find the value of |u| - |v|, we need to first find the values of |u| and |v|. We are given that |u| = 4 and |v| = 4.
Next, we need to find the angle between u and v when placed tail to tail. This can be done using the dot product formula:
u · v = |u| * |v| * cos(theta)
where u · v is the dot product of u and v, |u| and |v| are the magnitudes of vectors u and v, and theta is the angle between u and v.
In this case, the dot product u · v is given by:
u · v = |u| * |v| * cos(90)
Since the cosine of 90 degrees is 0, the dot product simplifies to:
u · v = 4 * 4 * 0 = 0
Therefore, the dot product of u and v is equal to zero.
Now, let's calculate |u| - |v|:
|u| - |v| = 4 - 4 = 0
Hence, the correct answer is 0, which is not among the provided answer choices.