Vector and magnitude problem

[fiziks09]

Homework Statement

A little assistance with this question:-

A vector, B, when added to the vector C = 3i + 4j 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?

Homework Equations

The Attempt at a Solution

i found the magnitude of C to be 5 i.e.

sqrt(3^2 + 4^2)= 5

since the question says this magnitude is equal to that of the resultant vector and taking the unit vector of B to be (x)i + (y)j; i equated it to 5 so i can try to solve for x and y i.e

(x+3)i + (y+4)j = 5

this is where i got stuck..

please any help will be very appreciated .. thanks

 

[rock.freak667]

So the vector B added to C is B+A=(x+3)i + (y+4)j

if the (B+A) points in the positive y-direction, then what should 'x' be?

When you get that, then apply |B+A| = |C|

 

[fiziks09]

i think x would be zero right? if dat's right what wuld y be??
Also ur notation is a bit confusing.. what is the vector A?? Also the vector in the positive y direction is supposed to be the resultant vector i.e B + C BUT u wrote B + A..i'm kinda confused there..

 

[rock.freak667]

i think x would be zero right? if dat's right what wuld y be??
Also ur notation is a bit confusing.. what is the vector A?? Also the vector in the positive y direction is supposed to be the resultant vector i.e B + C BUT u wrote B + A..i'm kinda confused there..

Sorry, I meant to type 'C', replace 'A' with 'C' is all.

you would have (x+3) being zero.

 

[rwisz]

I would approach this problem by first understanding the concept of vectors and their magnitude. A vector is a quantity that has both direction and magnitude. In this case, the vectors C and B are represented by the components (3i + 4j) and (xi + yj), respectively.

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude (or length) of a vector is equal to the square root of the sum of the squares of its components. Therefore, the magnitude of C is indeed 5, as you calculated.

To solve for the magnitude of B, we can use the given information that the resultant vector (when C is added to B) is in the positive y direction and has a magnitude equal to that of C. This means that the x component of B must be zero, since it is not contributing to the positive y direction.

Using this information, we can rewrite the equation as:

(0)i + (y+4)j = 5

From this, we can see that the y component of B must be equal to 1, since 4 + y = 5. Therefore, the magnitude of B can be calculated as:

sqrt(0^2 + 1^2) = 1

Therefore, the magnitude of B is equal to 1.

In summary, the magnitude of B is 1, since the resultant vector is in the positive y direction and has a magnitude equal to that of C, which is 5. I hope this helps with your homework problem. Remember, when solving vector problems, it is important to carefully consider the given information and use the appropriate equations to come to a logical solution.