Part I. Vector a'(0,1,0), b (1,0,1) calculate (2 points for each question, 10 points in total) (1)a+ b, (2) 3а , (3) The length of a', (4) The cross product a'x b, (5) Prove vector(-2,2,2) is perpendicular to a'x b

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: (1) Find the area of the triangle and indicate its type.

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Q: A river is flowing in a straight line from the point A(1,3) to the point B(5, 1). A town is located…

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Q: Q3) If P(2,-2, 1) , Q(3,-1,2) and R( 3,-1,1) ノ の)ind the area of the triangle determined by the…

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Q: ors are parallel u= and U= None of the others \(\) 6 \(\) -3 \(1) 2 10) 3

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Q: what is the magnitude of the vector

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Q: Find an equation E = 0 or inequality E‡0, where E' is an expression involving z and y, such that (x,…

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Q: Let(vector u)=(-2,-3), (vector v=(-3,-5) and vector w=(-2,-3). Find the vector x that satisfies…

A: u=(-2,-3)v=(-3,-5)w=(-2,-3)Calculating x:

Q: 5. In each case, find the equation of the line with the given properties. (a) Passing through the…

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Q: O Find a vector orthogonal to both (-2, 1, 0) and to (0, 1, –5) of the form

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Q: The line through the points the points (xo,Yo, Zo) and (x1,y1, z1) be parametrized by the function T…

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Q: prove using vectors that the points (0),2 -2- (B2,0, -2, C, (2,2-,10) represent the vertices of a…

A: We have to check weather the given points are Vertices of Traingle or not.  After that we have to…

Q: Q2/ (a) Let A (2,3,0) and B (-1,- 2,- 4) be two points. Find the vector AB in terms of the standard…

A: The detailed solution is as follows below:

Q: (a) is spanned by the vectors 10 Determine whether the vector v = --()-- [] and or not. 8 (a)…

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Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). O a. cos Cos cos-() O d. cos-() Ос.

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Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

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Q: -> If the projection of a = i-2 +3k on b = 2î+ ak is zero, then the value of 2 is (A) (B) 1 - 2 (C)…

A: Use the dot product to find the projection.

Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

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Q: Prove using vectors that the points represent the vertices of a triangle then (1) Find the area of…

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Q: The second picture is the result from other question, and I need to use that result with this…

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Q: ector Operations) Given vectors =, √ = and =, show (√x) = ( x )

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