Give the equation of the line in vector form, parametric form and symmetric form. The line through the point (1,−5,0) and parallel to the line given by r(t)=⟨ 8−3t, −10+9t, −1−t ⟩
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Give the equation of the line in
The line through the point (1,−5,0) and parallel to the line given by
r(t)=⟨ 8−3t, −10+9t, −1−t ⟩
Given line is
The direction ratios of given line are proportional to <-3,9,-1>.
Since the required line is parallel to given line, therefore, the direction ratios of the required line is also proportional to <-3,9,-1>.
We know that the equation of line passing through (x1 ,y2) and having direction ratios <a,b,c> in symmetric form is
Therefore, equation of required line in symmetric form is
Now, equation in parametric form is
Now, we will find equation is vector form
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