Find the vector and the cartesian equations of the lines that passes through the origin and `(5, 2, 3)`.

Options

A. ` r = 5hati - 2 hatj+ 3 hatk , 5 x =- 2 y = 3z `
B. ` r = lamda ( 5 hati - 2 hatj + 3 hatk ) , 5x = -2y = 3z `
C. ` r = lamda ( 5hati - 2 hatj + 3hatk ) , ( x ) ) / ( 5 ) = ( y) / ( - 2 ) = ( z ) / ( 3 ) `
D. None of the above

Answer

C

Explanation

Here, ` r = 0 + lamda ( 5 hati - 2 hatj + 3 hatk - 0 ) `
` r = lamda ( 5 hati - 2 hatj + 3 hatk ) " "`…(i)
[which is a vector equation]
Now , put ` r = x hati + h hatj + z hatk `
` therefore x hati + y hatj + z hatk = lamda ( 5 hati - 2 hatj + 3 hatk ) `
` rArr ( x ) / ( 5 ) = ( y ) / (- 2 ) = ( z ) / ( 3 ) = lamda `
Which is cartesian form of required line.