 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, find the equation of the line which passes through the point 1, 2, 3 and is parallel to the vector 3i plus 2j minus 2k. First of all let us understand that vector equation of a line passing through a point and parallel to a given vector b is given by r vector is equal to a vector plus lambda multiplied by b vector. Now in this equation a vector is the position vector of the given point and r vector is the position vector of an arbitrary point p on the line and lambda is the parameter. Now this is the key idea to solve the given question. Let us now start with the solution. Now we are given that line passes through the point 1, 2, 3. Let us assume that a vector be the position vector of this given point. So we can write let a vector be the position vector of given point and we know coordinates of given point are 1, 2, 3. Now we can write a vector is equal to i plus 2j plus 3k. We are also given that line is parallel to 3i plus 2j minus 2k. So we can write let b vector is equal to 3i plus 2j minus 2k. Now using key idea we get the vector equation of the given line is r vector is equal to a vector plus lambda multiplied by v vector. Here r vector is the position vector of an arbitrary point p on the line. Now substituting these components for vector a and vector b in this equation we get r vector is equal to i plus 2j plus 3k plus lambda multiplied by 3i plus 2j minus 2k. Now in this equation lambda is a real number. So this is our required equation. This completes the session. Hope you understood the solution. Take care and have a nice day.