A figure is translated using the vector (-3, 7). What translation vector would move the image back to its original position?

Q: Define the term Parallel Vectors?

A: Parallel vectors: The vectors that are parallel if they have the same direction.

Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by

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Q: What is meant by the term translation in vectors?

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Q: Write three properties of parallel vectors p and q.

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: Find a unit vector having the same direction as the given vector. (-7, 7)

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Q: Find a unit vector in the same direction as v= (28,-21).

A: A unit vector in the direction of (a, b)

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)

A:

Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: photo attached

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

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: Use vectors to determine whether the points are collinear. (4, −2, 7), (−2, 0, 3), (7, −3, 9)

A: Formula: the vectors a, b and c are collinear if detabc=0.

Q: Write the vector v = ⟨2, -4, 4⟩ as a product of its magnitude and a unit vector with the same…

A: Given vector is  v=2,-4,4 Magnitude of vector v  is v=(2)2+(-4)2+(4)2=4+16+16=36=6 Now, unit vector…

Q: Write a vector equation for the line segment from P to Q. 4

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Q: Find the magnitude of the vector. (-3, – 7)

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Q: Rotate the vector (5,1) 90° clockwise about the origin. ([ ? ],[ ])

A: We need to rotate the following vector 90° clockwise about the origin x,y = 5,1

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: Find the direction of the vector, in degrees, of the vector 21 - 21. No need to indicate the un

A: Recall; Let ai+bj be the vector, Direction of the vector is θ=tan-1ba We have, a=2, b=-2

Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: If vector v is represented by an arrow, how is -3v represented?

A: Given: If vector v is represented by an arrow. To find: How is -3v represented?

Q: Determine the tail of the vector whose head is(1, 2). Make a sketch.

A: Given the vector 26 and tail of the vector is (1,2). We need to find the head of the vector.

Q: Given a vector with initial point (−8, 3) and terminal point (5, −5), find an equivalent vector…

A: In the question we have to find an equivalent vector with initial points (0,0).

Q: How long is the shadow cast by a 540-foot tower when the sun's rays follow the vector [6,10,-27]?…

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Q: Find the vector pointing in the direction opposite that of (6, –8) with length 20.

A: The given vector  6,-8 For a given vector v, to find a unit vector u in opposite direction of v…

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: The given vector is -2,5.

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Find the magnitude of this vector (-8,8)

A: Given vector is  The magnitude of this vector is

Q: Find a vector in the same direction as (-5, 2, –3) with magnitude 6.

A: In this question , firstly we can find the unit vector of the given vector and after that we can…

Q: Determine the head of the vector;whose tail is (−3, 2). Make a sketch.

A: Consider (x, y) as the head of the vector. Then  -25=xy--32-25=x+3y-2

Q: Use vectors to determine whether the points are collinear (3, 4, −1), (−1, 6, 9), (5, 3, −6)

A: we have to use the vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,-6) are…

Q: Sketch the vectors

A: Solution : The magnitude  of |a| , |b|, |c| are  |a|=a1+a2|b|=b1+b2|c|=c1+c2 a=(-3)2+22     =9+4…

Q: Find the unit vector with the opposite direction of a⃗=(8,−10,3,−1,9,3)

A: We have to find the unit vector with the opposite direction of a→=8,-10,3,-1,9,3.

Q: Express the vector -8i-4j-8k as a product of its length and direction.

A: Given vector v→=-8i-4j-8k

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 vector equation of the line that passes through A(5,-4) and B(1,-1)

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

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

A:

Q: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

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

A: Consider the points: P=1, -2Q=3, 0

Q: The unit vector that has same direction as the vector from the point A(6, 8) to the point B(4, 10)…

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Q: Find the magnitude of the vector (9, 12).

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Q: Find a unit vector u in the direction opposite of (-8,-4,-9). u =

A: Given vector is -8, -4, -9 We have to find a unit vector u in the direction opposite of the given…

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: Let the initial point Pp1,p2 and the terminal point Qq1,q2.The component form of a vector…

Q: Find the unit vector with same direction as  ⟨ 6, 11 ⟩

A: We find the magnitude of  ⟨ 6, 11 ⟩ first

Q: when we decompose the vector , what would the vertical component be?

A: Use the decomposing concept of a vector.

Q: Find the vector in vl that has magnitude 8| and is in the opposite direction of (-3, –5, 1). v =||…

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Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below