B- If you have a vector perpendicular to the plane of P(1,-1,0) , Q(2,1,-1) nd R(-1,1,2) find: 1. PQ x PR 2. The area of the triangle Unit vooton

Q: Find the normal vector to the plane that contains the point (1, 1, 3) and the line r(t)=(0,1,…

A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

Q: Verify that the two planes are parallel. -x + 6y + 3z = 8 1. x + 2y + z = 9 Find the normal vector,…

A: Let's find.

Q: If p (x, y, z) = x² + y? + z2, what is the unit vector in the direction of Vy (1, 2, 3? )undefined…

A: To find the unit vector in the direction of  ∇φ1,2,3, whereφx,y,z=x2+y2+z2

Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 + 3y + z = 5 Find the normal vector, n,,…

A:

Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

A:

Q: 1) In the triangle that determined by the points P.Q and R, find a unite vector perpendicular to…

A:

Q: Hhewet Fint projection and Vector projiction ofBonto Afar: A-B, angte between A andBslength_of - -A=…

A:

Q: Qe A) Find the Vector 5 unit length in the direction of vector perpendicu lar to the dane which…

A: Normal vector we have to find out.

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 7 -…

A:

Q: Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

Q: Howed Find efuation fer fendicular to the vector from origin to A. of the plane through…

A:

Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A:

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

A:

Q: (a) Find the y-intercept of the line in 2- space that is represented by the vector equation r = (3 +…

A: Given : a) The line in 2- space that is represented by the vector equation r = (3 + 2t)i + 5tj .

Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w - x -y+ 3z 0, %3D…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 − t,   y =…

A: Given :              Vector v parallel parallel to the line x=3-t, y=-1+2t , z=-2.

Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: • We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

A: We have to show the steps for the above equation.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 4 -…

A: Given, The equation of the line x = 7t, y = 4-t, z = 3+9t We have to find the coordinate of the…

Q: Q/ find all unit vectors parallel to the yz plane and perpendicular to the vector V= 5i - j + 2k ?

A: Given,   A vector V= 5i - j + 2k.

Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

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

Q: What is a vector that is normal to the plane 4x+6(y-100)+7(z-200)=20? O A. 4i+6j-20 k O B. 8i+ 12 j…

A: Given query is to find the normal vector.

Q: Suppose that ∇ƒ(x, y, z) is always parallel to the position vector x i + y j + z k. Show that ƒ(0,…

A:

Q: H.W: Triangle with points P(1,-1,2) , Q(2,0,-1) and R(0,2,1), find: 1. Area of the triangle. 2. a…

A:

Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

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

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: OX is a trapezium.OX=a,XY=b,OZ=c.M is mid point of OX.N is point such that Z and Y are straight…

A: Given:  OX→=aXY→=bOZ→=c ON:OY=k:1

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 -…

A:

Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

A:

Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: Q/ Find the Unit Vector perpendicular to the Plane 2X+22-4Y=3

A: An equation of a plane 2X + 2Z - 4Y = 3 To Find: Unit vector perpendicular to the  given plane…

Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

A:

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. %3D N =…

A:

Q: . Let 7 - " be the separation vector from a fixed point (a', y', z') to the point (x, y, z). Show…

A: we have,  fixed point x',y',z'=r' and point x,y,z =r  r→-r→'=x-x'i^+y-y'j^+z-z'k^ a…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 4…

A: The equation of the line is x=7t, y=4-t, z=1+9t The equation of the line in symmetric form  is…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 2t x + 3y + z = 7 Find the normal…

A:

Q: Q1. A- Find the cross product (uxv) of vector (u = i – 2j + 5k) and vector ( v=). Are the two…

A: Topic = Vector If the cross product of two vectors is zero it means both are parallel to each other.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 6t, y = 7 –…

A:

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

Q: Verify that the two planes are parallel. -x + 6y + 3z = 5 -** 1 -x+ 2y + z = 6 Find the normal…

A:

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A: