Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3 -6 -6 -3

Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

A:

Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

A:

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

A:

Q: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

A:

Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Find the projection of vector A=(6,7) along vector B=(1,4).

A:

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

A:

Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

A:

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

A:

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection,…

A: We have to determine the vector that specifies the velocity at which the pathogen is evolving…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

A:

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

A:

Q: Let x and y be two orthogonal vectors. Then prove that +

A:

Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

A:

Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

A:

Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O

A: I have append the formula in solution part

Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

A:

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

Q: Construct the vector -a-2 b having initial point P.

A:

Q: Find the equation of the plane in xyz-space through the point P = (5, 4, 3) and perpendicular to the…

A: NOTE: Refresh your page if you can't see any equations. . the normal vector is  . the given point…

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

A:

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

A:

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O

A:

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

A:

Q: Find the orthogonal projection of the vector a (-9,-8, 7) in the direction of the (-3,-5,-2). vector…

A:

Q: Find a vector x whose image under T,

A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O

A: