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Solved in 3 steps with 3 images
- Compute the orthogonal projection of v = [-6 5 1 ] Onto the line L through [ -2 6 -7] and the originParametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is, find a function t → z(t), a ≤ t ≤ b such that the range of the function is the set of all points of the said line segmentFind the point on the graph of z = 2x^2 − 3y^2 at which vector n=⟨8,−12,1⟩ is normal to the tangent plane.
- write the equation of the plane with normal vector n passing through the given point in the scalar form ax + by + cz = d. n = (−1, 2, 1), (4, 1, 5)Find the scalar equation for the plane passing through the point P=(−4, 2, 10) and containing the line L defined byx = −8+14ty = 6+4tz = 12Suppose LMN->L'M'N'. If L(-8, 3) and L' is located at (-10, 8). What is the x value of the translation vector that maps LMN onto L'M'N'
- Find the image of the line that passes through the point (1, 1) and is parallel to the vector v = (1,−1) under the affine transformation T(x, y) = (x − y + 1, x + y + 2)Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3 ĵ+4 k.Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).