Question

Use an example to verify that a*(b + c) = a * b + a * c for all vectors a , b.

Please help! Thanks :)

Answer 1

is that cross product of vectors.

Answer 2

I dont know, I copied exactly how the question is written

Answer 3

R u k with cross and dot product of vectors.

Answer 4

Sure

Answer 5

If * is for scalar multiplication then we need to use dot product of vectors to prove it.
Let a=2i+3j+4k, b=i+2j+3k and c=3i+4j+5k.
b+c=(1+3)i+(2+4)j+(3+5)k=4i+6j+8k
a.(b+c)=2*4+3*6+4*8=8+18+32=58
a.b=2*1+3*2+4*3=2+6+12=20
a.c=2*3+3*4+4*5=6+12+20=38
a.b+a.c=20+38=58
Hence the result.

Answer 6

Ok, thanks! :)

Answer 7

yw.