4. Given 3 points: A(2, 1, 1), B(2, 2, 2), and C(4, 2, 2), compute the normal vector for the triangle ABC. Show step-by-step computation involved.

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

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Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: 6. Let a = (1, 0,3) and u = (2,-1,5). a.) (5 pts.) Evaluate projau. b.) (5 pts.) Find a vector that…

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Q: Find values of a and b, for which the following vectors are parallel: (8, a + b, 6), v = (4, 3, 2a —…

A: Given:   u = ⟨ 8 , a+b , 6 ⟩     v = ⟨ 4 , 3 , 2a - b ⟩

Q: Order the following vectors by increasing magnitude. (3,4) (0,-6) (-2,4)

A: Given vector is (3,4) , (0,-6) and (-2, 4). We have to order the vectors by increasing the…

Q: 1. Add the following three vectors to find the resultant vector, R: šj = (-2,0)m, .ž= (0,–5,)m, .řz…

A: 1.   x1¯  =  (-2,0)mx2¯  =  ( 0, -5)mx3¯   =  (3,0)m Now , In the East - west direction ,  we deal…

Q: Let P(-1, 1, 3) and Q(-3, 1, 5) be points in R3. Find the components, magnitude and direction angles…

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Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: 3. Add the vectors shown.

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: 2. For v = (5,-2) and w = (3, 4), find v+w, v - w, v/2, -w and make one sketch labeling all 6 of…

A: Given,           v=<5,-2> and w=<3,4>

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Find the cross product of the vectors ä = and b = .

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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: 38. Find the component form and magnitude of the vector with beginning point at (-2, 1) and end…

A: It is given that, the vector begins from point (-2,-1) and terminates at point (1,3).

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

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Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

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

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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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: 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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Q: Find two vectors in R³ which are not in the Span Please be sure to justify your reasoning. { [ 1 2…

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