4. (30 points) Given two distinct constant vectors a := (a1, a2, 3) and b :=...

 

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4. (30 points) Given two distinct constant vectors a := (a1, a2, 3) and b := (b1, b2, b3), consider the set of all position vectors r := (x, y, z) satisfying 15 (r a) (r b) = | |a b|. - (1) (a) The set of such r represents a sphere with radius R >0 centered at c = (C1, C2, C3). More specifically, r satisfies an equation written as (x-c)+(y-c2)+(zC3) = R. Determine R and c. = (b) Assuming a = (0,7, 2+ 3) and 6 = (-2, 3, 2 - 3), compute R and c in the previous question. 4. (30 points) Given two distinct constant vectors a := (a1, a2, 3) and b := (b1, b2, b3), consider the set of all position vectors r := (x, y, z) satisfying 15 (r a) (r b) = | |a b|. - (1) (a) The set of such r represents a sphere with radius R >0 centered at c = (C1, C2, C3). More specifically, r satisfies an equation written as (x-c)+(y-c2)+(zC3) = R. Determine R and c. = (b) Assuming a = (0,7, 2+ 3) and 6 = (-2, 3, 2 - 3), compute R and c in the previous question.

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a To find the radius R and the center c c1 c2 c3 of the sphere we can first expand the given equatio... View the full answer