Question

Obtain the magnitude of 2A - 3B if A = hati +hatJ- 2 hat k and b = 2 hat I - hat j+hat k .

Answer 1

Magnitude of 2A - 3B is 3√10 units.

•It is given that ,

A = i + j - 2k

B = 2i -j +k

•Now on multiplying A by 2

we get ,

2A = 2i + 2j -4k

•On multiplying B by 3

we get ,

3B = 6i - 3j + 3k

•Subtracting 3B from 2A

2A - 3B = -4i + 5j -7k

•Magnitude of vector ai + bj +ck

is given by √(a²+b²+c²)

•so, magnitude of 2A - 3B will be

|2A - 3B| = | -4i + 5j -7k |

|2A - 3B| = √[(-4)² + (5)² + (-7)²]

|2A - 3B| = √( 16 +25 +49)

|2A - 3B| = √90

|2A - 3B| = 3√10 units

•Magnitude of 2A - 3B is 3√10 units .