Let T1 : x +y + 2z = 1 and T2 : x – 2y – z = -2 be planes in R³ and let L be the line of intersection of T and T2. a) Find a vector equation for L. b) Find the minimum distance from the point Q(2, –1,3) to the line L

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

A:

Q: Find a vector equation with parameter tt for the line of intersection of the planes x+y+z=4x+y+z=4…

A: What is Plane: A plane is a flat, two-dimensional surface that never ends in mathematics. A plane is…

Q: Use the vector cross product to nd the equation of the plane in R3 containing the three points…

A: Points are  4,1,2,1,-1,1,5,2,3

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

A: .

Q: Let L be the line passing through the point P(−4, −3, 4) with direction vector d=[-3, 3, 0]T, and…

A:

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

A:

Q: Let L be the line with parametric equations x = 2+t, y = 5-2t, z = 4 + 3t. Let S be the plane that…

A: Given L is the line with parametric equations x = 2 + t , y = 5-2t , z = 4 + 3t . Let S be the plane…

Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

A:

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Determine a vector equation for the line of intersection of the planes: 9z - 6x = 63 and 4x - 6y +…

A:

Q: A line, in R³ which passes through the point (xo, yo, zo) and with the direction vector (a, b, c),…

A:

Q: e) Find an equation of the plane that contains the line L: 1=1-t, y= 2 +t, := -3t where t eR nd the…

A: The answer is given as follows:

Q: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

A:

Q: 1-x 2+3 Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : = y + 1 = 3 2…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

Q: Let L be the line passing through the point P(1, -1, -2) with direction vector d=[3, −4, 0]T, and…

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.