Problem 7. Investigate how one could multiply vectors in a meaningful way and give one or several possible definitions of products of vectors in the plane. Justify your choice and explain your reasoning.

Q: 1 4 (a) Determine the cross product of the vectors vi = 2 and v = -2 -4 3 Draw a diagram of the…

A: Solution of the given question is like asVectors in point form

Q: when I do the dot product of vectors a and c, and of vectors b and c, they aren't perpendicular…

A: The vectors are ,             a→ = (1,1,1)   ,   b→=(-1,0,1)  ,   c→= (1,-2,1) all are perpendicular…

Q: We know that a line can be described by two points or by a single point (a, b, c) and vector v that…

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Q: Using the same vectors v = (1,3, 2) and w = (3,5,6) and the same poin P= (8,4,-2). Find the equation…

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Q: would two independent vectors span a plane whereas two dependent vectors span a line?

A: If two vectors are linearly dependent:

Q: We know that there are two ways to multiply vectors: the vector and scalar product. How about vector…

A: Vector division is not possible .

Q: Which of the following are true of vector math? a)  The dot product between a vector and itself…

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Q: Find the volume of the parallelepiped determined by the vectors a č = (2, 4, 1). (3, 5, – 1), 6 =…

A: The volume, V , of a parallelepiped is calculated using the scalar triple product, V=c·(a×b) . Use…

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: 1. Find the equation of the plane. the points. Don't use three (1,2,1), (2,6,3), (0, 1,-1) which…

A: 1:  2: Note: We have taken d as common and taken  it to the other side of the equation.

Q: det pC-1,2,-1) and Q(2,-7,8) be two points in three dimenonal space. Use vectors to fird the points…

A: Vector form of a point: Let (a, b, c) are any point in 3D- space. Then this point can be expressed…

Q: Is the vector ?⃗ = ⟨−1, −2, 3⟩ perpendicular to the plane 3? + 6? − 9? + 5 = 0? Please give full…

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Q: Part C Find the angle b that the vector C makes with vector A. Express your answer in terms of some…

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Q: Two forces are acting on a point. The first force has a horizontal component of 5 newtons and a…

A: The complex number z=x+iy can be plotted in the complex plane by moving x units along the real axis…

Q: 1. What vector points from the origin to the point (4, 3, -1)? 2. Write (-3, 0, 2) as a sum of two…

A: Given : Point : ⟨ 4 , 3 , - 1 ⟩  Sum : ⟨ -3 ,0,2⟩

Q: 6. What are the advantages and disadvantages of algebraic vectors compared to geometric vectors?

A: Explanation:

Q: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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