00:01
Hi, in the question we have to prove that gradient of a x b is equal to b .gradient x a minus a gradient x b.
00:23
So, we will take lhs on taking lhs we will have gradient vector dot vector a x vector b.
00:34
So, this can be further written as summation of i cap del by del x of a vector cross b vector.
00:44
Since, we know that del by del x of a vector cross b vector can be written as del a vector by del x multiply by b vector plus a vector multiply by del b vector by del x.
01:03
So, we can write for above expression as summation of i cap del a vector by del x multiply by b vector plus a vector multiply by del b vector by del x.
01:20
So, from here we can further write this as summation of i vector del a vector by del x multiply by b vector plus summation of i vector multiply by i vector i cap a vector multiply by del b vector by del x.
01:45
So, this is further equal to summation of i del a vector by del x multiply by b vector minus summation of i cap del b vector by del x multiply by a vector.
02:04
Now, since we know that curl a vector can be written as gradient vector multiply by a vector this is further can be written as summation of i del by del x multiply by a vector...