Let T1 : x +y+ 2z = 1 and T2 : x – 2y – z = –2 be planes in R³ and let L be the line of intersection ofT1 andT2.a) Find a vector equation for L.b) Find the minimum distance from the point Q(2, –1,3) to the line L

Answered: Image /qna-images/answer/1c3bda32-24d0-4faa-8869-b610949bd212.jpg

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

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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

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

Q: 1. Find a unit vector perpendicular to the line passing through the points (1, 0, -3) and (2, 1,…

Q: Directions. Show the complete solution and avoid erasures. A. Determine which of the following are…

Q: 11. Let / be the intersection of the two planes 2x - 3y + 4z = 2 and x-z = 1 a. Find a vector…

A: Let l be the intersection of the following two planes(a) To find a vector equation of l.(b) To find…

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…

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 +…

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

Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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…

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot 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…

Concept explainers

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.

Question

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
T1 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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector-valued Function$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Let L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane r + 2y + 3z = 0. Find the y coordinate of the point of intersection of L and the plane 6x – 3y + 2z = 14
Let L be the line passing through the point P(−1, 1, 5) with direction vector d=[4, −1, 0]T, and let T be the plane defined by 5x+y-2z = 25. Find the point Q where L and T' intersect. Q=(0, 0, 0)
Let L be the line passing through the point P(1, 2, −1) with direction vector d=[-2, −3, −4]T, and let T be the plane defined by −3x+5y-2z = −17. Find the point Q where L and T intersect. Q=(0,0,0)
a) Find the plane equation which contains the line L given by x = 1- t, y = 1+ 2t, z = 2– 3t and the point (-1,1, 2). b) Let Q be the plane 2x + y+z = 4. Find the component of a unit normal vector for Q projected on a unit direction vector for the line L of part (a).
Consider the lines I = -1+ 2s l2 : y = s 3- I - 5 l1: 2 and z = 5+ s I. Find two unit vectors that are parallel to l1.
Let L, be the line given by the intersection of two planes 2x- y+z = 1 and x – y = -2 and let L2 be the line given by parametric equation x = 2 – t L2 : y = 3 – 5t z = t If u denotes the direction vector of L1 and uz denotes the direction vector of L2. Then (a) Find the vectors u and uz. (b) Find the dot product of the vectors u and u2. (c) Find the cross product of the vectors u and u2.
Find a vector equation, in terms of the parameter t, for the curve of intersection of the surfaces z = 42²-9y² and z = 2x + 3y.