Express v = ⟨5, −3, 2⟩ as a sum of orthogonal vectors such that one of the vectors has the same direction as u = ⟨1, 1, −8⟩. Prove that your vectors are orthogonal. (Hint: Find projuv, then form a triangle and use vector properties to find your other perpendicular/orthogonal side. You may NOT use the triangle as proof of your vectors being orthogonal.)

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

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Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

Q: What is the zero vector?

A: We have to define

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: find the diJ tance betueen the vectors

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Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: 3. Write ū as a sum of vectors, one in the direction of and another orthoganal to a. 18 [4] -5 [3³]

A: The given vector .The objective is to write the vector as a sum of vectors one in the direction of…

Q: Find the dot product of vectors and .

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Q: The vectors (2,10, 4) and (1, 3, x) are orthogonal if and only if x= -8. Ignore "Give your reasons"…

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Q: Find two independent vectors both of which are perpendicular to i = 3

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Q: Q4) Determine if the vectors below are independent. Justify your answer. -3° - ,V2 = [2. v, = |0|…

A: Given that:      v1=002, v2=05-8, v3=-341

Q: The scalar multiplication of a vector by a positive value results in another vector having the same…

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Q: The vectors and are orthogonal. True O False

A: Let a→=-3, 2b→=4, 6