Find the vector v = PQ. P = (10, 1, 5) Q = (0.5, -5, 4.5)

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: the a position vector( r) locates at points x-35 and y=45 determine the value of r and direction of…

A: Here we use vector application.

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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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: 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: 1. Find a unit vector that has the same direction as the vector (-4, 2,4).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let v = (-3,5, –5). Find a unit vector in the same direction as v.

A: on solving this we get

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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Q: photo attached

A: Given point can be written in vector form as,

Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: Find the unit vector directed   from (2, -5, -2) toward (14, -5,3)   a. a = 0.3858, +0.923a, b…

A: Here we have to find a unit vector.

Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v…

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Q: photo attached

A: Given that a vector V goes from the origin to a point (5, -5).

Q: Find the indicated vector. Let u = (8, –5) , v = (2, – 1) . - Find -2u+v. о (-14, —11) O 17 O -5 О…

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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: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

A:

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: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with…

A: Given vectors u=(1, -3, 5)  v=(2, 1,-3)  And line passing of point (1, 2,3)

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: A figure is translated using the vector (-3, 7). What translation vector would move the image back…

A: i have provided solution in step2

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: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: Find the components of the vector V with point p1 (1,4,5,3). And its ending point p2 (2,5,86) I need…

A: Given point is : p1=1,4,5,3 and p2=2,5,8,6 To find the component of the vector V.

Q: (c) Same direction as the vector from the point A(-1,0,4) to the point B(4,3, 3). 1 i + 2 w = k - 6.

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Q: Find the vector v = PQ. Р- (2, 1,4) Q = (-8.25, -4.25, 8) v =

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Q: Find the sum of the given vectors. а - (5, -1), ь - (-1, 8) a +b = 4,7 Illustrate geometrically. y

A: We have

Q: 6. Find the unit vector in the same direction as v. If u = (-12,8) and v = (-5,-12), find:

A: Consider the vectors u=<-12, 8>,    and    v=<-5, -12>. Need to find the unit vector in…

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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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: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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Q: Determine if the vector is a linear combination of the remaining vectors. Explain the steps.

A: We will check whether the vector v is linear combination of others or not.

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 the length of the vector. v - (9, 12)

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Q: If the vector v has initial point P, what is its terminal point? V3 (23, -5, 13), Р(-6, 4, 2) (х, у,…

A: vector= terminal point - initial point P= initial point=(-6,4,2) v=(23,-5,13) terminal point =…

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

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Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

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Q: . Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14).

A: Given that: Two points are (4, 2, 2) and (7, 6, 14)

Q: Find a unit vector that has the same direction as the given vector. (-8, 8, 4)

A:

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

A: Consider the points: P=1, -2Q=3, 0

Q: Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14)

A: The solution is given below in the next step:

Q: Find the indicated vector. Let u - (-3,-7) --8, -1). Find -2u - 3v.

A: To find -2u-3v :

Q: Find a vector normal to (0,2,3) and (-3,2,0). Choose the correct answer below. O A. (-6,9,6) В. (-6,…

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Q: Determine the angle between the vectors a = (4, 5, 2) and b = (-3, 6, 0)

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Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

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Q: Which vector gives the direction vector of a line given by vector v = (-3,-5, 1) + t(7,2,3)

A: Let us consider the vector form a line r→=a→+tb→ Here, a→ is a position vector and, b→ is a…