The "→" of the following vector is omitted, and the product of quantity is represented by *.

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.