Question

Vector B~ has x, y, and z components of 8.9, 4.1, and 2.7 units, respectively. Calculate the magnitude of B~ .

Answer 1

The magnitude of vector B~ with components 8.9, 4.1, and 2.7 is calculated using the Pythagorean theorem in three dimensions, resulting in a magnitude of approximately 10.16 units.

Step-by-step explanation:

To calculate the magnitude of vector B~ with the given x, y, and z components of 8.9, 4.1, and 2.7 units respectively, we use the three-dimensional version of the Pythagorean theorem. This theorem can be summarized in the equation for the magnitude of a vector, which is Magnitude B = √(Bx² + By² + Bz²). Plugging in the given components, we have:

• Bx = 8.9
• By = 4.1
• Bz = 2.7

Magnitude B = √(8.9² + 4.1² + 2.7²) = √(79.21 + 16.81 + 7.29) = √103.31 = 10.16 units

Therefore, the magnitude of vector B~ is approximately 10.16 units.