SORRY, i wrote this question wrong before ...
u, v, w are UNIT VECTORS. the angle between u and v is 25 degrees and the angle between vector v and w is 35 degrees.
find (v+w-3v). NOTE: vector u and w are on opposite sides of vector v.
I think you have partially corrected your question.
what about the v+w-3v ?
Where does u come into the picture?
v+w-3v would simply be w - 2v
To find the value of (v+w-3v), we first need to determine the values of v and w. However, since only the angles are given, we cannot directly determine the vectors u, v, and w.
To proceed, let's assume that vector u lies on the opposite side of vector v as vector w, as mentioned in the note. We can then use the given angles to find the values of v and w.
Given that the angle between vectors u and v is 25 degrees, we can use the dot product formula to find the cosine of that angle:
cos(angle) = u · v
Since both u and v are unit vectors, their magnitudes are 1. Thus, the dot product simplifies to:
cos(25 degrees) = 1 * 1 * cos(25 degrees)
cos(25 degrees) = cos(25 degrees)
Therefore, the value of the dot product is cosine of 25 degrees.
Using the same approach, we can find the dot product of vectors v and w using the angle between them as 35 degrees.
cos(35 degrees) = v · w
At this point, we don't have enough information to calculate the exact values of v and w, but we can express them in terms of their magnitudes and the angle between them, similar to how we dealt with u and v.
Now, let's simplify the given expression (v+w-3v):
(v + w - 3v) = v - 3v + w
Combining like terms, we get:
(v + w - 3v) = -2v + w
Therefore, the value of (v+w-3v) is -2v + w.
To further simplify the expression or find the exact values of v and w, we would need more information about the magnitudes of v and w or the relationships between the vectors.