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Determine the vector equation for the line, given the cartesian equation of a line is ?

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Concept:

Equation of a line in cartesian form:- 

Equation of a line in vector form:-  

where,  and 

Calculation:

We have,

Cartesian equation:- 

⇒       ------- equation (1)

⇒            -------- equation (2)

Comparing (1) and (2)

⇒ x1 = -5, y1 = 7, z1 = -3

⇒ a = 3, b = 2, c = 2

⇒ 

⇒ 

Equation of line in vector form:- 

⇒ 

∴ The vector equation for the line is  

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