Give the equation of the line in vector form, parametric form and symmetric form. The line through the point (1,-5,0) and parallel to the line given by r(t)=( 8–3t, –10+9t, –1–t >

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

Q: The parametric vector v=(6-t)i+(9t+8)j represents a straight line. Find the equation of this line

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: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

A:

Q: et L₁ be the line passing through the points Q₁(-5, 2,-5) and Q₂(-14, -7, 1) and let L₂ be the line…

A:

Q: Find a polynomial of least possible degree having the graph shown. f(x) =D (Type your answer in…

A:

Q: rite the equation of the line passing through P with direction vector d in vector form and…

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: Write the vector and Cartesian (standard) equation of the line, given a point and slope below.…

A: Definition used -    Vector equation of a line -                 r=a+λd      Cartesian equation of a…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.