 Hi, and welcome to the session. Let's work out the following question. The question says the Cartesian equation of a line r 66-2 is equal to 3y plus 1 is equal to 2z minus 2 Find a the direction ratios of the line and be the Cartesian and vector equations of the line Parallel to this line and passing through the point 2 minus 1 minus 1 So let us see the solution to this question The given line is 6x minus 2 is equal to 3y plus 1 is equal to 2z minus 2 This implies 6 into x minus 1 by 3 is equal to 3 into y plus 1 by 3 is equal to 2 into z minus 1 Dividing by 6 we get x minus 1 by 3 divided by 1 is equal to y plus 1 by 3 divided by 2 is equal to z minus 1 divided by 3 therefore Direction ratios of the line are 1 2 3 this is our answer to the a part now Cartesian equation of a line the point a that is 2 minus 1 minus 1 and Parallel to given line Is x minus 2 divided by 1 is equal to y plus 1 divided by 2 is equal to z plus 1 divided by 3 now for vector equation of This line position Vector of P is Vector a is equal to 2i cap minus j cap minus k cap Also vector v is equal to 1i cap plus 2j cap plus 3k cap So the required equation of the line is Vector r is equal to vector a plus lambda times vector b hence Vector r is equal to 2i cap minus j cap minus k cap Plus lambda times i cap plus 2j cap Plus 3k cap this is our answer to the second part And also this is the answer So I hope that you understood the solution and enjoyed the session have a good day