Question

What is the magnitude of A + B + Č, where Å = 1.00 i+ 4.00 i - 1.00 k, B = 3.00 î - 1.00 j - 4.00 k and Č = -1.00 i + 1.00 i?

A) 2.00
B) 6.78
C) 7.07
D) 8.12
E) 10.76

Answer 1

To find the magnitude of A + B + Č, we add the three vectors together component-wise and calculate the magnitude of the resulting vector. The magnitude of A + B + Č is approximately 7.07.

Step-by-step explanation:

To find the magnitude of A + B + Č, we need to add the three vectors together and then calculate the magnitude of the resulting vector. Given A = 1.00i + 4.00i - 1.00k, B = 3.00î - 1.00j - 4.00k, and Č = -1.00i + 1.00i, we can add them component-wise:

A + B + Č = (1.00 + 3.00 - 1.00)i + (4.00 - 1.00 + 1.00)j + (-1.00 - 4.00 + 0.00)k

= 3.00i + 4.00j - 5.00k

To calculate the magnitude of this vector, we use the formula: |A + B + Č| = sqrt((3.00)^2 + (4.00)^2 + (-5.00)^2)

= sqrt(9.00 + 16.00 + 25.00)

= sqrt(50.00)

The magnitude of A + B + Č is approximately 7.07. Therefore, the correct answer is C) 7.07.