Question 1199829: Evaluate
K.(i+j)
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Unit vectors i,j,k are defined as such
i = <1,0,0>
j = <0,1,0>
k = <0,0,1>
When combined, they form the 3D xyz axis.
i+j = <1,0,0> + <0,1,0>
i+j = <1+0,0+1,0+0>
i+j = <1,1,0>
Then apply the dot product
k dot (i+j) = <0,0,1> dot <1,1,0>
k dot (i+j) = 0*1 + 0*1 + 1*0
k dot (i+j) = 0
The zero dot product result tells us that vector k is perpendicular (aka orthogonal) to vector i+j
In fact, any linear combination m*i+n*j, such that m and n are scalars, will be orthogonal to vector k.
Answer: 0
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