Find the vector and the cartesian equations of the line that passes through the points`(3, 2, 5), (3, 2, 6)`.A. ` r = 3 hati - 2 hatj - 5 hatk , x - 3 = y + 2 = ( z + 5 ) / ( 11 ) `B. ` r = 3 hati - 2 hatj - 5 hatk , ( x - 3 ) / ( 0 ) = ( y + 2 ) /( 0 ) = ( z + 5 )/ ( 11 ) `C. ` r = 3hati - 2 hatj - 5 hatk + lamda ( 11 hatk ) , x - 3 = y + 2 = ( z + 5 ) / (11 ) `D. ` r = 3 hati - 2 hatj - 5 hatk + lamda ( 11 hatk ) , ( x -3 ) /( 0 ) = ( y + 2 ) /( 0 ) = ( z + 5 ) /( 0 ) `

Find the vector and the cartesian equations of the line that passes th

1.	Find the vector and the cartesian equations of the line that passes through the points`(3, 2, 5), (3, 2, 6)`.A. ` r = 3 hati - 2 hatj - 5 hatk , x - 3 = y + 2 = ( z + 5 ) / ( 11 ) `B. ` r = 3 hati - 2 hatj - 5 hatk , ( x - 3 ) / ( 0 ) = ( y + 2 ) /( 0 ) = ( z + 5 )/ ( 11 ) `C. ` r = 3hati - 2 hatj - 5 hatk + lamda ( 11 hatk ) , x - 3 = y + 2 = ( z + 5 ) / (11 ) `D. ` r = 3 hati - 2 hatj - 5 hatk + lamda ( 11 hatk ) , ( x -3 ) /( 0 ) = ( y + 2 ) /( 0 ) = ( z + 5 ) /( 0 ) `
Answer» Correct Answer - D We have, ` a= 3hati - 2 hatj - 5hatk ` and ` b = 3hati - 2 hatj + 6 hatk ` we know that, the vector equation of a line passing through the point having position vectors a and b is ` r = 3 hati - 2hatj - 5 hatk + lamda [ ( 3 hati - 2 hatj + 6 hatk ) - ( 3 hati - 2hatj - 5 hatk ) ] ` ` rArr r = 3hati - 2 hatj - 5hatk + lamda ( 11 hatk ) " " ...(i)` [which is the vector equation] Putting ` r = x hati + y hatj + z` hatk , in Eq. (i) , we have ` x hati + y hatj + z hatk = 3 hati - 2 hatj + (11 lamda - 5 ) hatk ` On comparing coefficients of ` hati , hatj and hatk ` on both sides, we get ` x= 3, y = - 2 ` and ` z = 11 lamda - 5 ` ` therefore (x - 3 ) / ( 0 ) = ( y + 2 ) / 0 = ( z + 5 ) / ( 11 ) ` which is the cartesian form of required line.

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