Given the vector a = 4.00i + 7.00j , find the magnitude of the vector.

Solution:

Given vector a = 4.00i + 7.00j

We know that the magnitude of the vector a + ib can be given as √(a₁² +a₂²)

Magnitude gives the length of the vectors. It is denoted by ||a||

Here, a₁ = 4.00 and a₂ = 7.00

|4.00 + 7.00j| = √(4.00² +7.00²)

|4.00 +7.00j| = √(16 + 49)

|4.00 +7.00j| = √65

Given the vector a = 4.00i + 7.00j , find the magnitude of the vector.

Summary:

Given the vector a = 4.00i + 7.00j , the magnitude of the vector is √65.