Q2: (a) Find the scalar and vector projection of ū along ủ, where u¯=(2, 3, 4) and v¯=(2, 2, 0). (b) Prove that the given planes are parallel or not, if yes then find the distance between them X + 3y + 2Z = 5, 2X+6y +4Z = 11.

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

Q: Use the function to find the image of v and the preimage of w. T(V,, V2) = (v, + V2, V - v2), v =…

A: Linear transformation: Let us consider a mapping T:V→W defined as T(v)=w where v∈V and w∈W [  v is…

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Calculate the triple scalar products w. (vx u) and u (w x v), where u = (7, 2, -1), v = (2, 8, -3),…

A:

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

A:

Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

A:

Q: Find the intersection of the line that passes through (0,3,-1), in the direction of…

A:

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

A:

Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = V2, V1 + V2, 2v, - v2 2…

A:

Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…

Q: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

A:

Q: Consider the R³ vectors v₁ = B. 3 23 V2 = 2 H -1 and v3 = D 3 (a) Find a linear dependence…

A:

Q: B Gruien Vectors i = (2,1₁-4), ✓ = (-340,2) w (11213). Find onthogonal projection of u + v along…

A:

Q: c that make the convolution equal to zero for the vector function F(x, y, z) = (2az + y – 5x)i + (2x…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.