Problem 18. Project the vector b onto the line through a. Check that e is perpendicular to a: (a) b = 2 and a = 2 1] (b) b 3 and a = 1

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

A: Here, the given points are A(3,5) & B(-3,-7)

Q: 1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(−2,…

A: According to our guidelines we can only solve the first question and rest of the questions can be…

Q: True or false? If v is a direction vector for a line L, then −v is alsoa direction vector for L.

A: True or false. If v is a direction vector for a line L, then -v is also a direction vector for L.

Q: 6. Explain in words how a student would determine the magnitude of the vector P[2, 3, 1]. There is…

A: To determine the magnitude of a vector P[2, 3, 1], a student would follow a simple set of steps. 1.…

Q: For what values of h the vectors -3.72%3D linearly independent are

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Q: 9. Find the dot product of the following pairs of vectors. a. u= (1, 3), v = (5,-2) b. = (9,-4), v =…

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Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

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Q: O ich of the following is a vector equation for the line through (-1,2,-2) and parallel

A: We have to find the vector equation for the line through (-1,2,-2)and parallel to…

Q: 5. For the vector OP = (1,4,-2), determine the direction cosine and the corresponding direction…

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Q: Let = [-3 1] and = [1 2]. Find the following vectors. [ ]]. ]]. u = 7y= = [1 w = 2x + 7y = [ v=27=…

A: Given: Let x→=[-3  1] and y→=[1  2].

Q: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

Q: Find the vectors T, N, and B at the given point. 16 (t) = (2, 룰,t), (4,-1, -2) T= N = B = 481 9'9'9…

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Q: ²=2+3+ k, v = -2i+ 3k. Find: (a) u v= (c) u x v= CONC (b) v. u= (d) 7 x = (e) Angle between 7 and 7…

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Q: Four students each made a statement about the equation of a line in R² given in vector form, 7 =…

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Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

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Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: 1. Find A-C|(B – D) using the following vectors: A= C= D=

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

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Q: Find the equation of line passing through point P(1, –1, 2) , the direction of the line is parallel…

A: The line passes through the pointP→ = i-j+2kThe line parallel to the lineV→ = i-2i+kThe vector…

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: roject the vector b onto the line through a. Compute the error e = b - p. Che at e is perpendicular…

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Q: Given a = = 5e2 and b = 2e₁ + €3, let C = a b. If the tensor C operates on another vector d = 7e1…

A: Given vectors are written as follows.Given that .Given that  operates on a vector .We need to find…

Q: 12. Given a point P(1,-2,-4) and a point P2(3,1,-5), find a unit vector that has the opposite…

A: Step 1:Step 2: Step 3: Step 4:  thanks...

Q: Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A−¹,…

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Q: 1) Check whether the vectors 효-1 33 5], -[3 10 6 T T Va = [2 7 3 2]' are line orly independent.

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Q: 10. Let a = (a₁, a2, a3), b = (b₁,b2, b3), and = (C₁, C2, C3) and y be a scalar. Prove the following…

A: Prove the associative property and distributive property.