Question

please give me full solution of this question​

Answer 1

Answer:

1.) A+B = 2i + 6j + k

|A+B| = sqrt( 2² + 6² + 1²)

= sqrt( 4 + 36 + 1)

= √41

Answer matched.

2.) A-B = 4i + 2j - 11k

|A-B| = √ 4² + 2² + (-11)²

= √16 + 4 + 121

= √141

Answer matched.

3.)

A+B = 2i + 6j + k

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

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

2A = 6i + 8j - 10k

A = 3i + 4j - 5k

|A| = √3² + 4² + (-5)²

= √9 + 16 + 25

= √50

Answer matched.

4.) A+B = 2i + 6j + k

B = (2i + 6j + k) - A

B = (2i + 6j + k) - (3i + 4j - 5k)

B = -i + 2j + 6k

|B| = √(-1)² + 2² +6²

= √1 + 4 + 36

= √41

Answer matched.

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

= -3 + 8 - 30

= -25

Answer matched.

6.) A×B =

$\left[\begin{array}{ccc}i&j&k\\3&4&-5\\-1&2&6\end{array}\right]$

= ( 24 + 10)i - (18 - 5)j + ( 6 + 4)j

= 34i - 13j + 10k

Answer matched.

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