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Homework Statement
show that points P, Q and R are in a straight line
P (1, -3, 4)
Q ( 2, 2, 1)
R (3, 7, -2)
and find the vectors ## \vec{PQ} ## and ## \vec{QR} ##
Homework Equations
The Attempt at a Solution
In proving that the points are in a straight line, we might be able to use dot product.In a straight line, means that the two vectors are parallel, (either in the same direction or opposite direction)
According to my math textbook it would appear that in the case of angle between vectors being zero degress, from there it follows that the vectors are parallel.
I was wondering about the second case when the vectors are in opposite direction but also parallel, wouldn't the angle between the vectors be 180 degrees?
From my understanding of parallel ( or in a straight line) in geometry, both cases may be possible for these vectors.
My textbook mentiosn only the 0 degree angle case
In any case it would seem to be prudent to compute the dot product of PQ and QR, and then find out the lengths of the vectors, and then finally find out what the angle actually is.
my textbook was Engineering Mathematics: Croft, Davison and Hargreaves.
Here is a quote page 219
If vector a and vector b are parallel vectors, show that a⋅b = |a| |b| . If a and b are orthogonal show that their scalar product is zero.
solution:
If a and b are parallel then the angle between them is zero. Therefore a ⋅b = |a| |b| cos(0deg)