Please explain thoroughly. A vector, B, when added to the vector C= 7i + 5j yiel

Question

Please explain thoroughly.
A vector, B, when added to the vector C= 7i + 5j yields a resultant vector which is in the positive y direction and has a magnitude equal to that of C. What is the magnitude of B?
A. 5.3 B. 15 C. 8.6 D. 7.9 E. 16 Please explain thoroughly.
A vector, B, when added to the vector C= 7i + 5j yields a resultant vector which is in the positive y direction and has a magnitude equal to that of C. What is the magnitude of B?
A. 5.3 B. 15 C. 8.6 D. 7.9 E. 16 Please explain thoroughly.
A vector, B, when added to the vector C= 7i + 5j yields a resultant vector which is in the positive y direction and has a magnitude equal to that of C. What is the magnitude of B?
A. 5.3 B. 15 C. 8.6 D. 7.9 E. 16
A vector, B, when added to the vector C= 7i + 5j yields a resultant vector which is in the positive y direction and has a magnitude equal to that of C. What is the magnitude of B?
A. 5.3 B. 15 C. 8.6 D. 7.9 E. 16

Explanation / Answer

D. 7.9

First you need to find what's the magnitude of C,

Mc = sqrt(x^2 +y^2) = sqrt(7^2 +5^2) =8.60

In order to have the same magnitude and be in the y axis the resulting vector must be equal to 5j.

If you subtract the resulting vector and vecto C you'll find the vector B that satisfy this problem,

R = C + B --> B = R - C

B = (0-7)i + (8.60-5)j

B = -7 + 3.6j

Magnitude of B = sqrt((-7)^2 +(3.6)^2) = 7.87 = 7.9

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