Question

If A vector = 2 i cap + 3 j cap + 2 k cap and B vector = 3 i cap + 2 j cap + 4 k cap , find out
i) A vector * B vector
ii) B vector * A vector
iii) (A vector + B vector ) * (A vector - B vector)

Answer 1

1-:A= 2icap +3 jcap+2kcap
B= 3 Icap + 2 jcap+4 kcap
A×B =(2icap +3 jcap+2kcap)×{3 Icap + 2 jcap+4 kcap)
0+4 kcap-8jcap -9 Icap+0+12 Icap +6jcap-4icap+0
-icap -2 jcap +4kcap
2 -:
B×A={3 Icap + 2 jcap+4 kcap)×(2icap +3 jcap+2kcap) = {0+9kcap-6jcap -4kcap+04 Icap+ 8 jcap-12 Icap +0
5 k cap+2. Jcap-8 Icap
3-:(a+b)× (a-b)
= (5 Icap+5jcap+6 kcap)×(-icap+jcap-2kcap)
(0 +5kcap+10 Icap+5kcap+10 Icap -6 jcap-6icap + 0
= 10 kcap +14 icap - 6 jcap

Answer 2

Answer:

The question can be answered in the following way:-

(2icap+3jcap+2kcap)

x (3icap+2jcap+4kcap) =

4kcap-8jcap-9kcap+12icap+6jcap-4icap =

8icap-5kcap-2jcap or

8icap-2jcap-5kcap

The easier way to solve this is given in the attachment. U can check that if u want : )

Explanation: