r(t)=e^t sin t + e^t cos t + 3

Find the unit Tangent vectors, unit Norm vector and binomial vector of the following vector functions. r(t)=e^t sin t + e^t cos t + 3

[Dyuman Joshi]

What have you attempted yet?

Answer 1

[Aditya Srikar]

Consider the given vector r(t)

Let r′(t) = d[r(t)] / dt

Let x(t) = r′(t)

The unit tangent vector will be

T(t) = x(t) / |x(t)|

Where |x(t)| represents magnitude of vector x(t).

Let y(t) = T′(t)

The unit normal vector will be

N(t) = y(t) / |y(t)|

Where |y(t)| represents magnitude of vector y(t).

Binormal vector is the cross product of unit tangent and unit normal vectors.

B(t) = T(t) × N(t)

Hope it helps !