Let a and b be two vectors. Prove that (b – proja (b)) · a = 0. Hint: Use the definition of the vector projection to rewrite the formula.

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: Calculate [1, 2, 2] x [5, -5, -1] -

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Q: what will be the direction of -k x -i ?

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

Q: = (2, -1) and v= (-2,3). Sketch u and v. Then sketch (show how the vectors are adding up) and…

A: Given, u=2,-1,v=-2,3

Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: For the matrix N = 9 22 4 3 7 1, find three different non-zero vectors that are in the null space of…

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Q: For the matrix N = Answer: 9 22 4 3 7 1 4 11 3 etry this question below find three different…

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Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: Let a = (-2, 0, 5) and b = (-3,- 2, 4). Find the angle between the vectors (in degrees).

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Q: Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and…

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Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: For which a are the vectors ⟨2,a,1⟩ and ⟨1,−2,4⟩ perpendicular?

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Q: a/(a + 3) x af а.) b.) (ā - 5)7

A: Recall if you can: Dot product of two vectors is a scalar A scalar times a vector is still a vector…