What is the angle between vectors A=i+j+k and B=i+j?
1 Answer
Jul 13, 2017
Explanation:
We're asked to find the angle between two vectors, given their unit vector notations.
To do this, we can use the equation
rearranging to solve for angle,
where
#vecA * vecB# is the dot product of the two vectors, which is
#vecA * vecB = A_xB_x + A_yB_y + A_zB_z#
#= (1)(1) + (1)(1) + (1)(0) = color(red)(2#
#A# and#B# are the magnitudes of vectors#vecA# and#vecB# , which are
#A = sqrt(1^2 + 1^2 + 1^2) = color(green)(sqrt3#
#B = sqrt(1^2 + 1^2+ 0^2) = color(purple)(sqrt2#
Therefore, we have