describe the motion of the particle if normal

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at ${\displaystyle (1,3,0),(-2,0,2),\text{and}(-1,3,-1)}$.

Find the vectors T, N, and B at the given point.
$r(t)=<t^2,\frac{2}{3}{t}^3,t>$ and point $<4,-\frac{16}{3},-2>$

Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R
b) Find the area of the triangle PQR

Find the cross product $a\times b$ and verify that it is orthogonal to both a and b.
$a=(2,3,0),b=(1,0,5)$

Identify the surface with the given vector equation. r(s,t)=${\displaystyle (s,t,t^2-s^2)}$
eliptic cylinder
circular paraboloid
hyperbolic paraboloid
plane
circular cylinder

Find direction numbers for the line of intersection of the planes x+y+z=1 and x+z=0

For any vectors u, v and w, show that the vectors u-v, v-w and w-u form a linearly dependent set.