S2 =13 y = kx + b Space and Verify S₂ = [(x, y) {R²: y = kx +b] change multiplication to is vector uⒸv = (u₁₁u₂ @ V₁, V₂ ) = (U₁ + V₁, U₂₁ V₂ - b Cu = C (u₁₁u₂) = (cu₁, cu₂-cb+b) by confirming 10 axioms

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

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 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: the cylielied 1.15) EXPRESS THE VECTOR K = (x^²√²³y + xy²5₂ coorddicta syster & eveluet it at the…

A: x=ρcos⁡ϕ  ,  y=ρsin⁡ϕ  ,  z=zThe position vector, r→=x ax→+y ay→+z…

Q: Determine the following value: F20 + F30 1. 2. F34 3. F67

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Find  vector z + vector y if vector z= and vector y= . graph

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Q: Q4\ Find the vector if its magnitude equal √90 and its unit vector is 4i 5j 7k + √90 √90 √90 -

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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: Find a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

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Q: Express the vector 12 x+ÿ. = [15] as a linear combination of a = 2 1 and y= -17 -2

A: Given

Q: A= (-5,12) B=(4,6) Assuming A and B as vectors, calculate the projection of vector B onto vector A.

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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: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: When multiplying a scalar and a vector: |ha|=|ā| when A |xa|=|||ā| when > + 0 and + 0.

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Q: 4. Express PQ-RO+SR-PS+RS as a single vector.

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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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