1) The orthogonal vectors u and V of the following are a) u = (1,0,1) and v= (0,1,1) b) u (3,0,-1) and v = = (2,2,1) c) u = (1,1,1) and v = (-1,-1,-1) d) u = (-2,1,5) and v = (-1,3, −1) 2) The unit vector in the direction from the point P(-4,1,2) to the point Q (2,3,-1) is a) (6,2,-3) b) (−6, —2,3) c) (6,-2,3) d) (6,2,3) 3) Which of the following points lies on the line L: x = 1-t, y = 2 + 3t, z = 5+ 2t? a) (1,2,4) b) (3,-4,1) c) (0,5,3) d) (-1,2,9)

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Determine (x, y, z) for each figure. Then find the component form of the vector from the point on…

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

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Q: Which is the vector perpendicular to the vectors n₁ = (2, -3,0) and n2 = (1,7,9)?

A: Given that: n1→=2,-3,0, n2→=1, 7, 9 The perpendicular to the vectors n1→ and n2→ is required.…

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

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Q: why are the position vectors of D, E, F (b+c)/2, (a+c)/2 ect and not D= (c-b)/2, E= (c-a)/2, F=…

A: The objective is to determine why are the position vectors of D, E, F are b+c2,a+c2, and…

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

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Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: determine nonzero vectors that are orthogonal to the following vector (b).  (1, -2, 3) c. (5, 1, -1)

A: Let the vectors be- u→=xi^+yj^+zk^v→=i^-2j^+3k^ For the vectors to be orthogonal-…

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

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Q: The vector v has initial position P and terminal pet P (2, 5); Q=D (-5,-1) v 7i+ 6j Ov- 6i+ 7j…

A: Let's Solve, Answer: Option D

Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

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Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

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Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: Consider the vectors v₁ ví = (1,2,3,0), v = (0,1,2,3) and vg = (2,3, 4, -3) Let (1, 1, 1, 1) w (a)…

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Q: A plane contains the point A(-1,2,5) and has direction vectors (2,-1,3) and (-3,1,5). Which of the…

A: Given:   Point : ( -1 , 2 , 5 ) Vectors : ( 2 , -1 , 3 ) and ( -3 , 1 , 5 )

Q: vector of the vector basis The coordinate (-4,3,1) in the B={u= (1,1,1); v= (1,0,1); w=(0,0,1) } is…

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Q: Find all vectors (x,y,z) that are orthogonal to the vectors (1,2,3) and (4,5,6). Find the vector in…

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Q: 5. Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2)…

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