[3] Let J1 = 2,72 = 2; and let B = (V1, V2) be the basis for a plane P = 3 %3D 1 span(01, v2) CR. What are the coordinates of the vector i.e. find (b3 || 5 Clearly identify b3 in your solution.

Q: Q2: (a) Find the scalar and vector projection of ū along ủ, where u¯=(2, 3, 4) and v¯=(2, 2, 0). (b)…

A: Given : u=2,3,4, v=2,2,0 we know that scalar projection of u along v is given by…

Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

Q: If the vector K ag+Lay+ Ma, shows the maximum increase rate and direction of the scalar Vat point…

A: If the vector Ka^x+La^y+Ma^z shows the maximum increase rate and direction of the scalar V at point…

Q: Resolve the vector of 300N at N25W into its rectangular components. Use right/left and up/down for…

A: To resolve the vector

Q: 21. Find the coordinate vector of x = with respect to the basis B = {v1, V2, V3} where vi =|1 V2 =…

A: Write x in linear combination of v1 , v2 , v3

Q: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

Q: Perform the following conversions. a) The line 5x + 7y - 35 = 0 to vector form. b) The plane [x, y,…

A:

Q: Q4) The vector product of two vectors is scalar product. F O T

A:

Q: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

A:

Q: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

A:

Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

A:

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

A:

Q: products

A:

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

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

A:

Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: Define a basis B = (ā,b, c) for R³, where -- 2 6= 1 3 Define P to be the plane spanned by d and b.…

A: To define a basis B=a→, b→, c→, we determine the determinant of matrix formed by vectors a→, b→, c→.…

Q: Let x = p+ su +tv be the vector equation of a plane in R³. Then the plane passes through the origin…

A: Vector equation of a plane:

Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

A:

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: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar 4u - (2v - w)

A: Given: u=-2i+3j , v=6i-j , w=-3i

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Find a scalar equation for the plane that contains the points P, Q and R

A: We know that equation of plane passing through three points A(x1,y1,z1),B(x2,y2,z2), C(x3,y3,z3)  is…

Q: Find the equation of the plane that passes through the point P(1, 0, 2) and contains the line whose…

A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

A:

Q: 3. Complete the following questions using the following planes T₂: 2x+4y-6z-2=0 m₂: 7x+14y-21z-7=0…

A:

Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: Find a vector function that satisfies the conditions r"(t) = 12ti – 31-/2j+2k, r'(1) = j, r(1) = 2i…

A: We have to find a vector function that satisfies the conditions…

Q: 1.20. Given the plane 4x +3y +2z = 12, find the unit vector normal to the surface in the direction…

A:

Q: Q2 Given the vectors r=3i+4j-5k and s=-2J-K, where the xyz coordinate frame is obtained by rotating…

A: The given vectors are:r=3i+4j-5ks=-2j-k We have to find the cross product r×s

Q: Consider the following graph. (4,5) 2 (1, 2) 3 (a) Find the component form of the vector v. (b)…

A: Given vector is as shown below :

Q: 4. Find the vector equation for a particle if A(t) = 6ti + 12t² j+ k, V(0) = 2i + 3j, and R(0) = 4k.

A: Given that At=6ti+12t2j+k,V0=2i+3j,r0=4k.

Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

A:

Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

A:

Q: Q4: Find the vector projection of u 6i + 3j + 2k onto v =i- 2j 2k and the scalar %3D component of…

A:

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y?…

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

A:

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

A:

Q: 1. Determine the vector component of A = 3a, + 2ag – 6as tangential to the cone. %3D

A: The vector is A→=3ar+2aθ-6aϕ. Generally, the vectors are shown as sketched below:   Instead of…

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

A: