# Problem with vectors

• Jan 7th 2013, 09:54 AM
MMCS
Problem with vectors
Question

Forces of magnitude 3 Newtons, 5 Newtons and 7 Newtons act along the vectors (-3,-2,-9) (8,5,-9) (4,-1,-9)

Find the x component.

I have the answer at 4.968 however i can not arrive at it, attached is my working out. d has been used instead of c.

i have the x components as 2.531, -2.774 and -6.93 however these are not correct as they do not equal the answer of 4.968

Thanks
• Jan 7th 2013, 10:35 AM
ebaines
Re: Problem with vectors
You need to find the x-component of each of the three force vectors, then add them. So starting with 3 N acting along (-3, -2, -9): the magnitude of this directional vector is sqrt(3^2+2^2+9^2) = 9.969, and the portion acting in the x direction is -3/9.969 = -0.3094. Multiply by 3N to get -0.928N. This is the amount fo force acting in the x-direction for the 3N force. Repeat this for the other two vectors and add, and you should get Fx = -0.928N + 3.068N +2.828N = 4.968N.
• Jan 7th 2013, 10:44 AM
MMCS
Re: Problem with vectors
ah this looks right, thank you. Can i ask why the -3 is divided by 9.969?
• Jan 7th 2013, 10:51 AM
ebaines
Re: Problem with vectors
What you really want is the directional vectors to be expressed as unit vectors (i.e. have magnitude 1). So that first directional vector is given as (-3, -2, -9) expressed as a unit vector is (-3/9.696, -2/9.969, -9/9.969), or (-0.3094, -0.2063, -0.9283). You should double check that this has magnitude of 1. Now you can multiply the x, y, and z components of this unit vector by 3 N to find the x, y, and z components of the 3N force.
• Jan 7th 2013, 10:53 AM
MMCS
Re: Problem with vectors
Thanks ebaines, cleared that up for me
• Jan 7th 2013, 11:50 AM
MMCS
Re: Problem with vectors
Hi Ebaines, is it possible for you to give me some help to get started on another question.

Three vectors

a = xi - 3j + 9K
b = -3i + xj - 10K
c = 9i - 10j + xk

Find the largest value of x for which the magnitude of the resultant is equal to 17.
I am given the correct answer of 8.564 but i dont know how to get that.

I have no working out to show for this as i dont know where to start, but some advice would be helpful

Thanks
• Jan 7th 2013, 12:15 PM
ebaines
Re: Problem with vectors
When you add vectors a, b and c the resultant is ((x-3+9)i, (-3+x-10)j, (9-10+x)k). Now write out the formula for the magnitude of this vector, and solve for x such that the magnitude is 17.