# Find the distance between the pair of points, Give the exact distance. Simplify completely. ( 3 , - 2 ) and ( 4,3 ) Question
Vectors and spaces Find the distance between the pair of points, Give the exact distance. Simplify completely. ( 3 , - 2 ) and ( 4,3 ) 2020-12-01
To find the distance between pair of points use the formula $$\displaystyle\sqrt{{{\left({x}{1}-{x}{2}\right)}^{{2}}+{\left({y}{1}-{y}{2}\right)}^{{2}}}}$$
The given value is (3,-2) and (4,3)
so
x1=3
y1=-2
x2=4
y2=3
So after applying the formula PSK=sqrt((4-3)^2+(3-(-2))^2) =sqrt((4-3)^2+(3+2)^2)ZSK
$$\displaystyle{\left({4}-{3}\right)}^{{2}}={1}$$
PSK(3+2)^2=5^2 =sqrt(1+5)^2 =sqrt(1+25) =sqrt26ZSK

### Relevant Questions Find the distance UV between the points U(7,−4) and V(−3,−6). Round your answer to the nearest tenth, if neces Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or $$\displaystyle{90}^{{\circ}}$$. u = (-1, -1, 8, 0), v = (5,6,1,4) Use $$\displaystyle{A}{B}←→$$ and $$\displaystyle{C}{D}←→$$ to answer the question. $$\displaystyle{A}{B}←→$$ contains the points A(2,1) and B(3,4). $$\displaystyle{C}{D}←→$$ contains the points C(−2,−1) and D(1,−2). Is $$\displaystyle{A}{B}←→$$ perpendicular to $$\displaystyle{C}{D}←→$$? Why or why not? The position vector $$\displaystyle{r}{\left({t}\right)}={\left\langle{n}{t},\frac{{1}}{{t}^{{2}}},{t}^{{4}}\right\rangle}$$ describes the path of an object moving in space.
(a) Find the velocity vector, speed, and acceleration vector of the object.
(b) Evaluate the velocity vector and acceleration vector of the object at the given value of $$\displaystyle{t}=\sqrt{{3}}$$ Find the angle between the vectors $$\displaystyle<{1},{3}>{\quad\text{and}\quad}<-{2},{4}>$$ Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).  Find the angles made by the vectors $$\displaystyle{A}={5}{i}-{2}{j}+{3}{k}$$ with the axes give a full correct answer Prove that $$\displaystyle{T}{\left({x},{y}\right)}={\left({3}{x}+{y},{2}{y},{x}-{y}\right)}$$ defines a linear transformation $$\displaystyle{T}:\mathbb{R}^{2}\to\mathbb{R}^{3}$$. Give the full and correct answer. 