Question

Derive the equation of line in space passing through a points and parallel to a given vector .b'' both in the vector and Cartesian form

​

Answer 1

Step-by-step explanation:

remark:- we know that if two lines are parallel then first line or second line will be the multiple of another.

ie in diagram,

AP =(lamba)b

Answer 2

Concept:

An item with both magnitude and direction is referred to be a vector. A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

Given:

A point on vector plane and a vector B

Find:

Derive the equation of line in space passing through a points and parallel to a given vector .b'' both in the vector and Cartesian form

Solution:

Let there be a line joining pint a anb. which is paralel to vector b

Then AP is parallel to b

also, AP=kb

where, k is a real number

Now, AP=OP-OA

⇒kb=r-a

or    r=a+kb

its cartesian equation will be

x-x₁/a=y-y₁/b=z-z₁/c=k

Therefore the the equations are x-x₁/a=y-y₁/b=z-z₁/c=k ( in cartesian form ) and r=a+kb(in vector form)

#SPJ2