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

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: Express the vector P, P2 in the form v = v, i+ v2j + v3k if P, is the point (- 7, - 3,1) and P2 is…

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Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: 1. Determine R21, the vector from P2(5, 2,–4) to P¿(3,–1,0). А. 4ах + ay · 6az В. 2а, + Зау — 4а, С.…

A: P25, 2, -4 & P13, -1, 0

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

Q: 3. Find a unit vector with the same direction as (3, 4).

A: If we devide each component of vector v by |v| we will get the unit vector Uv.

Q: find the component form of vector RS with the initial point R(3,-2) and terminal point S(3,3)

A: From the given problem:   Initial point R3,-2   Terminal point S3,3   So the component form of RS→:…

Q: 3. Find a vector equation for the line through (2, 7, −3) that is orthogonal to the plane 3x + y −4z…

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Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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Q: Given the two points A(1,2,3) and B(2,-3,4) which of the following is the vector equation passing…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 6- which of the vectors X-(1,2),Y =(0,1),Z =(-2,-4 ) ,W=(-2,1), U=(-6,3) are orthogonal ,in same…

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Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

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

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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: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: The vector with terminal point at P(-5,0,3) and initial point at Q(6, 2, –8) is equal to the…

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,…

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

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Q: 1. The vector in the opposite direction to u = (-1,0) and of half its length is 2. The vector of…

A: 1.The vector is u=<-1,0>2.The vector is v=<-4,5,-3>

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: Find a vector equation of a line passing through the point (-1, -2, 4) and perpendicular to both a =…

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Q: Find the vector equation of the line (a) through the point (1, −5) and parallel to the x-axis; (b)…

A: As per our guideline we are allowed to do 1 question and 3 subparts at a time. Please post other…

Q: If the vector v has initial point P, what is its terminal point? v = (0, 0, 3), P(0, 3, -3) (x, y,…

A: Let's find.

Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

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Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.