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(a) Find the distance between the skew lines l1 and l2 given with the vector equations...

(a) Find the distance between the skew lines l1 and l2 given with the vector equations l1 : r1(t) = (1+t)i+ (1+6t)j+ (2t)k; l2 : r2(s) = (1+2s)i+ (5+15s)j+ (−2+6s)k.

(b) Determine if the plane given by the Cartesian equation −x + 2z = 0 and the line given by the parametric equations x = 5 + 8t, y = 2 − t, z = 10 + 4t are orthogonal, parallel, or neither.

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