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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
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.
ah this looks right, thank you. Can i ask why the -3 is divided by 9.969?
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.
Thanks ebaines, cleared that up for me
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
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.