Find the angle θ between the vectors.?
u = 9j
v = -2i
θ=____________________
so I think this is right...
cos (theta) = dot product of vectors / product of the magnitude of the vectors
you want to write the vectors like: u = 0i + 9j and v = -2i + 0j
(i know it looks redundant)
so, magnitude is easy: for u, sq rt (0^2 + 9^2) = 9
for v, sq rt(-2^2 + 0^2) = 2
and the denominator will be 9*2 = 18
dot product takes the coefficients of i and multiplies them, then adds then to the product of the coefficients of v (sounds harder than it is)
(0*-2) + (9*0) = 0
so, cos(theta) = 0/18
therefore, cos(theta) = 0
and the cos = 0 at 90 degrees (if you know the unit circle, awesome! if not, calculator works too)
so you've got a 90 degree angle between these two vectors
hope this helps!
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Answers & Comments
so I think this is right...
cos (theta) = dot product of vectors / product of the magnitude of the vectors
you want to write the vectors like: u = 0i + 9j and v = -2i + 0j
(i know it looks redundant)
so, magnitude is easy: for u, sq rt (0^2 + 9^2) = 9
for v, sq rt(-2^2 + 0^2) = 2
and the denominator will be 9*2 = 18
dot product takes the coefficients of i and multiplies them, then adds then to the product of the coefficients of v (sounds harder than it is)
(0*-2) + (9*0) = 0
so, cos(theta) = 0/18
therefore, cos(theta) = 0
and the cos = 0 at 90 degrees (if you know the unit circle, awesome! if not, calculator works too)
so you've got a 90 degree angle between these two vectors
hope this helps!