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- Determine the divergence of the vector V=(x^2)yi-xyj+xyzk at (3, 2, 1)Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) parallel to the line through (2, 0, −1) and(4, 1, 3)
- Find the displacement vector with initial point A(-3,4) and terminal point B(1,1) and determine the modulusfind a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8), direction vector v = (1, 0, 1)Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).
- find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8), direction vector v = (2, 1, 3)Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\ x_2\end{array}\right]$ on the side How find a formula for the sheared vector $K(\vec{x})$. Draw analogously figure for horizontal shear like for vertical shear.A person on hang glider is spiraling upward due to rapidly rising air on a path defined by x²/9 +y²/9+z²=1 then determinea. Vector valued function that position the path.b. Unit tangent vector for ac. unit normal vector for ad. Curvature..
- Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).What is special about the derivatives of vector functions of con-stant length? Give an example.Find a unit vector pointing in the direction in which the maximum rate of change occurs for the following function at the given point. f(x,y)=2xsin^2(xy)at the point (2,1). Express your answer as a unit vector and round the value(s) to three decimals.