Vector differentiation

16 practice questionsIntegral CalculusStep-by-step solutions

Try a few

If $\vec{a}(t)$ and $\vec{b}(t)$ are differentiable vector functions of $t$ , which is the correct product rule for $\dfrac{d}{dt}(\vec{a}\cdot\vec{b})$ ?

\dfrac{d\vec{a}}{dt}\cdot\vec{b}+\vec{a}\cdot\dfrac{d\vec{b}}{dt}

\dfrac{d\vec{a}}{dt}\cdot\dfrac{d\vec{b}}{dt}

\dfrac{d\vec{a}}{dt}\times\vec{b}+\vec{a}\times\dfrac{d\vec{b}}{dt}

\dfrac{d\vec{a}}{dt}\cdot\vec{b}-\vec{a}\cdot\dfrac{d\vec{b}}{dt}

🔒 Answer + full step-by-step solutionUnlock free →

A particle's position is $\vec{r}(t)=3\cos t\,\mathbf{i}+3\sin t\,\mathbf{j}+4t\,\mathbf{k}$ (helical motion). Find its speed $|\vec{v}(t)|$ .

5

(constant)

\sqrt{9\sin^2 t+9\cos^2 t+16t^2}

, which varies with

t

3

7

🔒 Answer + full step-by-step solutionUnlock free →

A particle's position vector is $r(t) = (3t^2 - 2t)i + (t^3)j$ meters. Find the i-component of the particle's velocity vector at $t = 2$ seconds.

12

m/s

8

m/s

10

m/s

14

m/s

🔒 Answer + full step-by-step solutionUnlock free →

Master vector differentiation — not just preview it

All 16 questions with worked solutions, an AI tutor that explains every step, and games that make the drilling stick. Free to start.

Practice this topic free

No card needed · 10 free AI questions daily

Vector differentiation

Try a few

Master vector differentiation — not just preview it

More Integral Calculus topics