Question

13. The sum and difference of two vectors A and B are
→
Л ^
A A
Л ^
л ^
->
->
→ →
A + B = 2 i +6 j + k and A - B = 4 i + 2 j - 11 k. Find
(1) A + B (ii) | A - B (iii) | A | (iv) | B | (v) A.B
(vi) AⓇB.​

Answer 1

Answer:

A

+

B

= 2

i

^

+6

j

^

+

k

^

...(i)

A

−

B

= 4

i

^

+2

j

^

−11

k

^

...(ii)

Adding equations (i) and (ii) :

2

A

= 6

i

^

+8

j

^

−10

k

^

A

= 3

i

^

+4

j

^

−5

k

^

Subtracting (ii) from (i)

2

B

= −2

i

^

+4

j

^

+12

k

^

B

= −

i

^

+2

j

^

+6

k

^

Therefore,

∣

∣

∣

∣

A

∣

∣

∣

∣

= 5

2

∣

∣

∣

∣

B

∣

∣

∣

∣

=

41

A

.

B

= −3+8−30

= −25