Question

The sum and difference of two vectors A and B are B = 2 î+6j+ k and A-B=4i+2j-11 k. Find A x B.​

Answer 1

Given:-

• A+B= 2i + 6j + k + 4i - 2j - 11k
• A-B= 4i - 2j - 11k

To Find:-

• A.B

Solution:-

$A+B + A - B = 2i + 6j + k + 4i - 2j - 11k$

$= >2 A = 6i + 8j - 10k$

$= > A = 3i + 4j - 5k$

Now,

$= > A+B= 2i+6j+k$

$= >B= 2i+6j+k - A$

$= >B= 2i+6j+k - 3i - 4j + 5k$

$= >B= - i - 2 j+ 6k$

Magnitude of Vector A= $\sqrt{ {3}^{2} + {4}^{2} + { - 5}^{2} }$

$= > \sqrt{9 + 16 + 25} = \sqrt{50}$

Magnitude of Vector B=$\sqrt{ { - 1}^{2} + { - 2}^{2} + {6}^{2} }$

$= > \sqrt{1 + 4+ 36} = \sqrt{41}$

Scalar Product of A.B=$( 3i + 4j - 5k).( -i-2j+6k )$

$= > - 3 + 8 - 30$

$= > - 25$