A vector whose initial point is at the origin is called ---------------------------- a/an vector.

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

A:

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

A:

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

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

A:

Q: 2). Express the vector v with initial point P and terminal point Q in component form. P(-1, 4),…

A:

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

A:

Q: Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

A:

Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

A:

Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

A:

Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

A:

Q: Show that no linearly independent set of vectors can contain the zero vector.

A:

Q: Sketch the given vector with initial point (1, 6). u = (-7, -4)

A:

Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: The vector v and its initial point are given. Find the terminal point. = (4, -9); Initial point: (9,…

A: Given

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

A:

Q: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

Q: What is the component form of the vector with an initial point of (-2,5) and a terminal point of…

A: Given that ,  The vector with  Initial Point = (-2 , 5) Terminal Point = (7 , -3).

Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: Find the component form and length of the vector v that has initial point (3, −7) and terminal point…

A: Given: Initial point (3,-7) and terminal point (-2,5).

Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

A:

Q: Which vector in two-dimensional space has no corresponding unit vector?

A:

Q: a horizontal vector has initial point (-4,1) and has a magnitude of 7. What is the terminal point?…

A: The initial point of the vector is (-4, 1) and the magnitude of the vector is 7. Since it is a…

Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

A:

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: 1. The components of the vector, initial point P(-3, 4, 1) and terminal point Q(-5, 2, 2).

A:

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: A vector w has initial point (1, -5) and terminal point (-2, -3). Write w in component form.

A: We find the vector in component form when the initial and terminal points are given by simply…

Q: 2 Determine the tail of the vector 4 whose head is (3, –2, 2).

A: To determine- The tail of the vector 24-1 whose head is 3-22.

Q: 3. find the length of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2)

A: Solution :

Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

A:

Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

A:

Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

A:

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

A:

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

A: We will solve the problem

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

A:

Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

A:

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

A:

Q: Express the vector v with initial point P and terminal point Q in component form. P(-4, 6), Q(-9,…

A: Given that the initial point is P-4,6 and the terminal point is Q-9,-4. The objective is to find the…

Q: 1. The components of the vector, initial point P(-3, 4, 1) and terminal point Q(-5, 2, 2). 2. The…

A:

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

A: