Discuss: Different Coordinate Systems As was noted in the overview of the chapter, certain curves are more naturally described in one coordinate system than in another. You need to give directions to your house to a taxi driver. You need to give directions to your house to a homing pigeon.

An object moving in the xy-plane is acted on by a conservative force described by the potential energy function ${\displaystyle U(x,y)=\alpha (\frac{1}{x^2}+\frac{1}{y^2})}$ where ${\displaystyle \alpha }$ is a positive constant. Derivative an expression for the force expressed terms of the unit vectors ${\displaystyle \overrightarrow{i}}$ and ${\displaystyle \overrightarrow{j}}$.

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space
$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$

T must be a linear transformation, we assume. Can u find the T standard matrix.${\displaystyle T:{\mathbb{R}}^2\to {\mathbb{R}}^4,T\left(e_1\right)=(3,1,3,1)\text{and}T\left(e_2\right)=(-5,2,0,0),where{e}_1=(1,0)\text{and}{e}_2=(0,1)}$

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.

Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate A - B?

Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?

What is the projection of ${\displaystyle <6,5,3>}$ onto ${\displaystyle <2,-1,8>}$?

What is the dot product of ${\displaystyle <1,-4,5>}$ and ${\displaystyle <-5,7,3>}$?

Which of the following is not a vector quantity?
A)Weight;
B)Nuclear spin;
C)Momentum;
D)Potential energy

How to find all unit vectors normal to the plane which contains the points ${\displaystyle (0,1,1),(1,-1,0)}$, and ${\displaystyle (1,0,2)}$?

What is a rank $1$ matrix?

How to find unit vector perpendicular to plane: 6x-2y+3z+8=0?

Can we say that a zero matrix is invertible?

How do I find the sum of three vectors?

How do I find the vertical component of a vector?