In Exercises 1-8, find a. v•u, |v], |u| b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vector proj, u. 1. v = 2i – 4j + V5k, u = -2i + 4j – V5k 2. v = (3/5)i + (4/5)k, u = 5i + 12j 3. v = 10i + 11j – 2k, u = 3j + 4k || 4. v = 2i + 10j – 11k, u = 2i + 2j + k 5. v = 5j – 3k, u = i +j+ k 6. v = -i + j, u = V2i + V3j + 2k = 2i + V17j 7. v = 5i + j, u = 8. v = V3.

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A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

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Q: Dot Product and Projections in Exercises 1–8, find

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Q: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Q: In Exercises 1-8, find a. v.u, v], |u| b. the cosine of the angle between v and u c. the scalar…

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Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

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