Given the following two vectors perform the given operations

Given the following two vectors perform the given operations:
a = [5 -3 0], b = [-2 4 5]. ]. Find 2a b

Given the following two vectors perform the given operations:
a = [4 -2 0], b = [-2 4 5]. Find a x 3b

Solution

Sol:

2a=2 [5 -3 0]=[10,-6,0]=10i-6j+0k

b=[[-2,4,5]=-2i+4j+5k

dot product=2a.b=(10)(-2)+(-6)(4)+(0)(5)

=-20-24+0

2a.b =-44

cross product:

3b=3[-2,4,5]=[-6,12,15]

to findcrossproduct:

ax3b=i j k

4 -2 0

-6 12 15

=i[(-2)(15)-(0)(12)-j[(4)(15)-(0)(-6)]+k[(4)(12)-(-2)(-6)]

=i[-30-0]-j[60-0]+k[48-12]

=-30i-60j+36k

a x 3b =[-30,-60,36]