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- Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.Find a vector normal to the plane -2x - 3y = 12 - 4z.
- Find the coordinates of a point P on the line and a vector v parallel to the line (x + 3)/5 = y/8 = (z − 3)/6Find a nonzero vector normal to the plane z−3(x−5)=−4(2−y).Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.