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# Vector Equations

### Useful vector equations and practice problems

QuestionAnswer
What is a vector? A quantity that has magnitude and direction
What is a scalar? A quantity that has only magnitude.
What is the initial point in a vector is it its compenent form? (0,0)
If u (u1,u2) and v (v1,v2) what is u+v? (u1+v1, u2+v2)
what is the magnitude of v? The square root of (v1)squared + (v2)squared
If r(t) is a position vector for a particle with respect to time what is the velocity vector? dr/dt=v(t)
What is the absolute value of v(t) Speed
If v(t) is a velocity vector for a particle with respect to time what is the acceleration vector? dv/dt=a(t)
If a(t) is the acceleration vector for a particle with respect to time what is the velocity vector? v(t)=the antiderivative of a(t) + C
If v(t) is the velocity vector for a particle with respect to time what is the position vector? r(t)= the antiderivative of v(t) + C
If u=(7,3) and v=(-2,4) what is u-v ? (9,-1)
Write the vector from point P (3,-1) to point Q (2,4) as a linear combination (-1,5) -1i+5j
v(t)=(5t)i + (tsquared)j what is r(t)? r(t)=(5/2tsquared + C)i + (1/3tcubed + C)j
If r(t)= (ln(t)+1)i + (tsquared-1)j, find the distance traveled from t=0 to t=2 L=antiderivative of the square-root of (1/(1+t))squared + (4t)squared = 4.335
Created by: weier1