Dot Product of Two Vectors

Hi, I'm unsure on how to do this question:

Evaluate a . b
a = 3i + 4j
b = -4i + 3j

Thanks!

a . b= a1b1+a2b2
a1=-3
a2=4
b1=-4
b2=3

so a.b= 3*-4+4*3=0

The dot product is zero. This also means these two vectors are orthogonal/ perpendicular.

Hello nobodyuknow, recall the fact that dot product of i and j is zero.
So a.b = -12 i.i + 12 j.j
But i.i = j.j = 1
Hence the required a.b = 0

a.b = (3i + 4j) . (-4i + 3j) = -12 + 12 = 0

Since the dot product of given two vectors is 0, the two vectors are perpendicular.

be careful you could also define a "vector cross product" in three dimensions
vector multiplication is tricky, division almost impossible

and if they are complex vectors where i = square root of minus 1 , it is even harder