Problem with vectors . . . . .?

Question

Hi.

I have the vector 3i - 2j + 4k that describes the movement of a particle. I need to change this so that the particle moves along the same line but with speed 2.

How do I do this? I have the answer but I don´t know how to get it. The answer is in coordinates or vectors.

Please show your answer step by step and please explain what you are doing at each step.

Thank you!

Answer 1

Okeydoke. The vector in question has a magnitude of:

sqrt(3^2 + 2^2 + 4^2) (It's okay to ignore the negative part of negative 2, since you're squaring it.)

sqrt(9 + 4 + 16) = sqrt(29), or about 5.3. If we multiply each of the components by 2/sqrt(29), we'll have a vector pointing in the same direction, and with a magnitude of 2.

6/sqrt(29)i - 4/sqrt(29)j + 8/sqrt(29) k

Hope that helps.

Oh, and ted s... Since there isn't a variable, integrating and differentiating is going to be somewhat difficult. I think all they need to do is change the magnitude to 2.

Answer 2

you had better modify your vector since it is FIXED and does not describe movement...when you do then take the derivative, compute its magnitude, multiply the derivative by "2 / magnitude"...the new vector has speed 2...integrate this vector to get back to a position vector...compute the constant of integration by using a known point on the path of the particle.