In Cartesian space, the direction of the line (x, y, z) = (a, b, c) +r(d, e, f) is represented by the vector (d, e, f) or any nonzero multiple of this vector. Select one: True False

Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: Consider the points P(5, −2, 3) and q(−3, 0, 2) a. Write vector |op| using unit vectors. b. Write…

A: Basics of VECTOR are used.

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Given, vector a = (3, 4, -2), vector b = (2, -7, 1), and vector c = (-6, 5, 4). Evaluate |-2b x c|

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Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: a. Write the vector (23,-12, -19) as a linear combination of a₁ = (3, -2, -1), a2 (2, -3, -1) and ã3…

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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: In Problems 27 and 28, establish the given inequality. 27. If = 2, then = +6+8i| ≤ 13. 28. If = 1,…

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Q: For each pair of vectors, find U V.   . U = -i +j, V =-i - j

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Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

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Q: Plot the points in same three-dimensional coordinate system and determine whether u and v are…

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Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: The vectors a=⟨2,3,z⟩ and b=⟨1,2,z⟩ are orthogonal to c=⟨z,r3,−z⟩, where z and r are nonzero real…

A: Given:Vector a=2,3,z,b=1,2,z are orthogonal to c=z,r3,-z

Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: 5. Complete the table with the points of the image by applying the vector (-3, 5). Preimage A (-1,…

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Q: Find if the vector w = (-3,2,-6) can be expressed as a linear combination of the vectors v₁ =…

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Q: a. Write the vector (-4,-8,6) as a linear combination of a₁ = (1,−3,−2), ẩ₂ = (-5, -2,5) and a3 =…

A: The given vectors  and .(a) The aim is to write the vector  as a linear combination of the given…