Question

How do you Convert Cartesian to Vector?

Answer 1

Conversion of Cartesian to vector :

Step 1: Equation of line of Cartesian form

The Cartesian form of equation of a line passing through the point $(x_1,y_1,z_1)$ and having the direction cosines a, b, c is

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

Step 2 : Equation of line in vector form

$$\begin{gathered} \stackrel{\rightharpoonup }{r}=\stackrel{\rightharpoonup }{a}+\lambda \stackrel{\rightharpoonup }{b} \\ where, \\ \stackrel{\rightharpoonup }{a}=x_1\overbrace{i}+y_1\overbrace{j}+z_1\overbrace{k} \\ \stackrel{\rightharpoonup }{b}=a\overbrace{i}+b\overbrace{j}+c\overbrace{k} \end{gathered}$$

Step 3: Substituting the value of $(x_1,y_1,z_1),a,b,c$in vector form

$\stackrel{\rightharpoonup }{r}=(x_1\overbrace{i}+y_1\overbrace{j}+z_1\overbrace{k})+\lambda (a\overbrace{i}+b\overbrace{j}+c\overbrace{k})$

Hence, to convert Cartesian to vector need to follow these steps .