What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the vector a0 based at the origin and equivalent to a.

Q: The vector v = ⟨−1, 3⟩ and its Initial point: (4, 2). Find the terminal point.

A: Given: To Find: Terminal Point   Concept:

Q: Find the vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: B. Find the unit vector with the initial point P(-3,4,1) and terminal point Q(-5,2,2). Then find the…

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Q: How do I teach students to map coordinates on to vectors?

A: I am assuming that our discussion is restricted to 2D geometry. A typical vector will have a…

Q: photo attached

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

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: Determine the equations of the line (vector, parametric, Cartesian and general) that passes through…

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Q: 10

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

Q: The plane contains the point (2, −1, 6) and is normal to the vector &lt;2, −1, 6&gt;.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

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

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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 the…

A: follow next step

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

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: 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: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

A: Given problem:- Find an equation of the plane that passes through the point P(-8, -4,7) and has the…

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: 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: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Sketch the given vector with initial point (7, 5). %3 (4, 2) u =

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Q: Find the general form equation of the plane through the origin and perpendicular to the vector (4,…

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Q: What is the component form of the vector whose tail is the point (-1,5), and whose head is the point…

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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: Find a vector of length 3 pointing in the same direction as .

A: Find a vector of length 3 pointing in the same direction as 4,-3,-4

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

A: Consider the provided vector, 26 Whose head is 1,2. Determine the tail of the given vector.

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: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

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Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: From the graph we can se that the coordinates of point P is 5, 2 and the coordinates of point Q is…

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

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Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

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Q: What is the component form of the vector whose tail is the point (-3, 2) and whose head is the point…

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Q: Find the component form and magnitude of vector v. 7. Initial Point (12,-3) Terminal Point (4,-1)

A: We can find the answer as below

Q: What is the component form of the vector represented by 2a when = (-2, 3)? Enter the answer in the…

A: If we multiply by a constant to any vector then  magnitude of that vector will be changed.

Q: Consider the vector whose initial point is P( – 4, 3) and terminal point is Q(0, - 1). Find the…

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

A: Use the decomposing concept of a vector.

Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: Find the angle between the vectors [ -1, 1, 2] and [2,1,-1].

A: Consider the vector: v = −1,1,2w =…

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

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Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…