Find a vector equation and parametric equations for the line. (Use the parameter t.) the line through the point (7, 0, −4) and parallel to the line x = 4 − 4t, y = −1 + 2t, z = 6 + 9t r(t) = (x(t), y(t), z(t)) - ( =

Q: 13. Given the points A(3,5) and B(- 3, - 7), find a. the vector equation of the line. b. the…

A: Here, the given points are A(3,5) & B(-3,-7)

Q: Find parametric equations of the line perpendicular to the yz-plane passing through the point (5,…

A: The direction ratios  of lines perpendicular to the yz-plane are 1,0,0 We obtain the equation of…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: THE ANSWER IS IN THE EXPLANATION PART.FEEL FREE TO ASK ANY OF YOUR DOUBTS AND COMMENT IF YOU FACE…

Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find a parametric equation for the line that passes through the point P(-5,7,10), and is parallel to…

A: To find a parametric equation for the line passing through the point P(−5,7,10) and parallel to the…

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: We find the vector equation and the parametric equation for the line through the point (6,-7,4) and…

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

A:

Q: I 7. Find the vector and parametric equations of the line that passes through the points A(7,10,4),…

A:

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, or…

A:

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

Q: Find the parametric equation of the line that passes through the point P(2,4, –2) and is parallel to…

A: Parametric equation of line that passes through the point P(x0, y0, z0)& parallel to vector a =…

Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

A:

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Write parametric equations of the line L through the point P: (2, 0, -3) and parallel to the vector…

A:

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

A:

Q: Describe the graph of the equation. r = (6 – 21) i+ 10rj O It is a line in 2-space through the point…

A: Solution :-

Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: Find vectors u and v such that the parametric equation of the line y= mx + b can be expressed as…

A: Given that  equation of the line is  y= mx + b…