Question

The sum and difference of two vectors A and B are a + b is equal to 2 i + 6 J + K and a minus b is equal to 4 ICAP + 2 J - 11 k find the magnitude of each vector and the dot product of a and b

Answer 1

Answer:

hope ...it...helps...

Explanation:

Answer 2

Answer:

Magnitude of a = $\sqrt{50}$

Magnitude of b is = $\sqrt{41}$

Product of a and b is a.b = -25

Explanation:

We have been given

Two vector A and B is equal to

a + b = 2 i + 6 j + k

a - b = 4 i + 2 j - 11 k

( a + b ) + (a - b ) = ( 2 i + 6 j + k ) + ( 4 i + 2 j - 11 k )

2 a  = 6 i + 8 J - 10 k

a = 3 i +4 j -5 k

Magnitude of a is = $\sqrt{3^{2}+4^{2} + 5^{2}$

Magnitude of a = $\sqrt{50}$

( a + b ) - (a - b ) = ( 2 i + 6 j + k ) - ( 4 i + 2 j - 11 k )

2 b = -2 i + 4 j +12 k

b = - i + 2 j + 6 k

Magnitude of b is = $\sqrt{-1^{2}+ }2^{2} +6^{2}$

Magnitude of b is = $\sqrt{41}$

Now ,

Product of a and b is

a.b = (3 i +4 j -5 k ) * (- i + 2 j + 6 k)

a.b = -3 + 8 -30

Product of a and b is a.b = -25