The equaton of the line in vector and cartesian from that passes through the point with position vector ` 2 hati - hatj + 4hatk ` and is in the direction ` hati + 2 hatj - hatk ` are

Answer

D

Explanation

The equation of the line in vector from
` therefore r = 2 hati - hatj + 4hatk + lamda ( hati + 2 hatj - hatk ) `
Now, put ` r = x hati + y hati + z hatk `
` therefore x hati + y hatj + z hatk = ( 2 + lamda ) hati + ( - 1 + 2 lamda ) hatj + ( 4 + lamda ) hatk `
` rArr x = 2 + lamda, = - 12lamda , 2 = 4 - lamda `
` rArr ( x - 2 ) / ( 1 ) = ( y+ 1 ) /( 2 ) = ( z - 4 ) / ( - 1 ) `
which the required equation of the given line in cartesian form.