18!- Use the vectors to find the area of the triangle with vertex A(1,0,1), B(0,2,3) and C(2,1,0).

Q: (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? 2.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

A:

Q: Find the cosine of the angle between the vectors P1(x) = 1+ 2x -x² and p2 (x) = -2-x+ 3x2 with…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

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

A:

Q: Find a vector of length 5 in the direction opposite that of (3, –2, V3).

A: Let the given vector be              a=3i-2j+3k The vector in the direction opposite to a  is  -a.…

Q: Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the…

A: Let us consider an incomplete regular polygon of n sides and the same polygon after rotation. We…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

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

A:

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

A:

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: 2) How many different vectors are drawn here? -/

A: 3 vectors are same which has same direction and magnitude and other 2 vectors are same in direction…

Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

A:

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

A:

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: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: Give an example of vectors in R^3 that spans R^3. (show works)

A:

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

A:

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: 2 Determine the tail of the vector 4 whose head is (3, –2, 2).

A: To determine- The tail of the vector 24-1 whose head is 3-22.

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

A:

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and…

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |<u,v>|…

Q: Find the length of the vector.v = (2, 0, −5, 5)

A:

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

A:

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

A:

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A:

Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

A:

Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: Find the sum of the vectors (3,0,1) and (0,8, 0) and illustrate geometrically.

A: Solved below

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

A:

Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: Give a set of vectors that is linearly dependent for P3 Show your work.

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

A: