8. Let V = {(x,y)x,y e R}. Define addition on V as follows: (x,y)+(x₂,₂)=(x₂+2x₂-Ly,+ y₂ +2) e-mon privolla? D'BOE ( ot ent to asoma Find the zero vector.

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: 1. Let v = PQ where P = (3,4,0) and Q = (2, 3, 1) Find a vector u that is parallel to V but with a…

A:

Q: Q11. Consider the vector u, v, w defined by u = (1,1), v= (4,0) and w = (0,3) %3D %3D %3D a) Express…

A: Given: u=(1,1)v=(4,0)w=(0,3)

Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

A:

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

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: 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: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: Find any two non collinear vectors on the plane x-y-3z +6=0

A:

Q: 2. If X(-2, -6, 5) and Y(3, -4, 1) are two points in R³ , determine: a) XY b) | XY | in reduced…

A:

Q: 2. Find vectors v, w E R³ such that v + w = (1,3,7), v is parallel to (1, 0, 1), and w is orthogonal…

A:

Q: Let A(x,y,,z) and B(x,,y2; z,) be two known 3D points. The point M on the line AB divides the vector…

A: The vectors AB, AM and MB are collinear vectors. Therefore, consider the formula for the collinear…

Q: Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (5,-4)…

A: Solution:Given: ,            we have to find a unit vector  that is normal to the level curve of…

Q: 7. Let u = (2,1, −1) and v = (√√2, 1, 1). Find the decomposition of u into vectors that are parallel…

A:

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

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: 4. Write y as the sum of two orthogonal vectors, y, in L and y₁ in L Let y = YL = 1 and u = 2 7 Let…

A:

Q: Prove: iv. if (x, y) = 0 for all x € R², then y must be the zero vector.

A: