Question

Find the values of . (a) (4hatj) xx (-6hatk) (b) (3hatj).(-4hatj) (c) (2hati) - (-4hatk) .

Answer 1

4j × 6k = 24 î

3j . 4j = 12

2i -(- 4k) is simply 2i + 4k

a)

4j × 6k

•Let vector A = 4j

& vector B = 6k

•Now Cross product of two vectors i.e. Vector A and Vector B is denoted by A×B, which is given by

A × B = |A||B| sin(Q) n

•where |A| is magnitude of vector A

|B| is magnitude of vector B

Q is angle between Vector A and Vector B

•So, |A| = 4 & |B| = 6 also angle Between A & B is 90°

•so , A×B = 4×6×sin(90°) n

A×B = 24×1 n

A×B = 24 î

•where n is direction of A×B & is decided by right hand thumb rule.

b) 3j . 4j

•Let vector A = 3j

& vector B = 4k

•Now dot product of two vectors i.e. Vector A and Vector B is denoted by A.B, which is given by

A . B = |A||B| Cos(Q)

•where |A| is magnitude of vector A

|B| is magnitude of vector B

Q is angle between Vector A and Vector B

•So, |A| = 3 & |B| = 4 also angle Between A & B is 0°

•so , A.B =3× 4×Cos(0°)

A.B = 12×1

•Dot product of two vectors is a scalar quantity , so it does not have direction

c) 2i -(- 4k)

=> 2i + 4k

2i -(- 4k) is simply 2i + 4k