a*b
=(4i+3j)X(3i-4j)
=4i×3i-4ix4j+3ix3j-3jx4j
= 12i? -7ij- 12j?
∵ij is a simplex vector
∴i? =j? = 1
∵ij is perpendicular to each other (the product of the number of mutually perpendicular vectors is zero).
∴7ij=0
∴a*b=0
If you have a good understanding, you can solve it like this.
Because ij is a unit vector,
Then we use ij units as the xy axis.
At this time, the coordinates of vector ab are (4, 3) (3, -4) respectively.
(Coordinate expression of product of vectors: (x, y)*(m, n)=xm+ny)
Then we have a*b=4x3+3x(-4)=0.