1. Answer the following: (a) You are given a plane in space. How many distinct vectors of unit magnitude are perpen- dicular to this plane? (b) How many distinct vectors exist, all having unit magnitude, perpendicular to a given line in space? (c) If A is a nonzero vector, how many distinct scalar multiples of A will have unit magnitude?

Q: a= b=

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Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: 3. Find the magnitude, ||||, of each of the following vectors: a. = -51 + 12j b. = -i- j

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Q: Is the vector ?⃗ = ⟨−1, −2, 3⟩ perpendicular to the plane 3? + 6? − 9? + 5 = 0? Please give full…

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Q: (4) Show that L[u(v — 2)](s) = −²³. -38 +386

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Q: Question 3 Find a unit vector in the direction of the given vector. 20 -10

A: 3. To Find: The unit vector in the direction of the vector -2020-10

Q: 1. What vector points from the origin to the point (4, 3, -1)? 2. Write (-3, 0, 2) as a sum of two…

A: Given : Point : ⟨ 4 , 3 , - 1 ⟩  Sum : ⟨ -3 ,0,2⟩

Q: 18. A child throws a ball with a speed of 5 feet per second at an angle of 54° with the horizontal.…

A: Given Speed of a ball =5 feet per…

Q: 1. A vector is: a. a quantity whose magnitude can be completely specified by a number b. a quantity…

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