2. Consider the following vector 1 v= = [1, 0, √6 (a) Write a projection on this vector. Proof your claim! (b) Write the complement projection. Proof your claim! -1, 2]¹.

Q: 2. Find the angle between vector [2, -5,7] and vector [6,4,1]

A: Vector [2,-5,7] and vector [6,4,1]  We have to find angle between these two vectors

Q: Write the vector u = (2,10) in i, j form. Written in i, j form, the vector u = (2,-10) =

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Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: find the diJ tance betueen the vectors

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Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

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Q: 2. Find the unit vector in the direction of

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Q: . Consider the following vectors 7 -3 b₁ ( 1 ), b₂ = (-1), G₁ = ( 1 ) ₁2 = (-²). C1 , 5 2 and…

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Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: Obtain Vector v = 3î+ 4ftransformed with -1 1 3 2 –4]

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Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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