Consider the planes 2r + 2y+ 3=1 and 2r + 3 0. (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with positive first coordinate that is parallel to both planes. i+ j+ k (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes,r (t) = i+ j+

Q: Consider the planes given by the equations x + 2y – 2z = 1, 4x – y + 2z = 7. | (a) Find a vector i…

A: Given the equation of planes, x+2y-2z=14x-y+2z=7

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

A:

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

A:

Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: Consider the points A(-3, 4, 2) and B (8,-1, 5). (a) (i) Find AB. () Find AB (ii) 2 1 A line L has…

A:

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

A:

Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

A:

Q: A river is flowing in a straight line from the point A(1,3) to the point B(5, 1). A town is located…

A:

Q: (14) The straight line L passes through the origin O and is in the direction i+mj. The straight line…

A:

Q: 8n 8n players P₁, P2, P3, ..., Psn play a knock out tournament. It is known that all the players are…

A:

Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: (a) Find a vector equation and symmetric equations for the line through the point (0, 14, 10) and…

A: Approach to solving the question:We are given a point (0,14,10) and a direction vector d=(2,−3,9).…

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.