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- Simplify the following functions using a k-map.Write the equations for k-map(a-b-c-d)Let v be a vector whose coordinates are given as v = [vx, Vy, Vz. If the quaternion Q represents a rotation, show that the new, rotated coordinates of v are given by Q(0, Vx, Vy, Vz)Q*, where (0, vx, Vy, Vz) is a quaternion with zero as its real component.
- Two vectors from the vector space described in the previous prob- lem (polynomials defined on the interval [-1, 1]) are 1+1 and 1-1. Find an orthogonal set of vectors based on these two vectors.Determine if the vector is a gradient and if it is, find a function having the given vector as its gradient. 2xyi + (1+x²) j = 0Computer Graphics Develop an algorithm for calculating the normal vector to a Bezier surfaces at the point P(u, v).
- Question 8 Find the unit vector along the line joining point (2, 4, 4) to point (- 3,2, 2). A) -0.8703ax - 0.3482ay + 0.3482az В -0.8703ax - 0.3482ay - 0.3482az c) 0.8703ax - 0.3482ay - 0.3482az -0.8703ax + 0.3482ay + 0.3482azCreate K-maps and then simplify for the following functions 1) F(x, y, z) = xyz’ + x’yz + xyz6. Using the root vectors, work out the weight diagram of 10.
- Simplify the following function into product of sums form using a K-map. F(x,y,z) = ∑(0,5,7)Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 + 5v2), v = (1, -2, -3), w = (3, 9) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u,. Which of the following statements are then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un: O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector o + u, is not equal to u: Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + o 0, which contradicts that u, is an additive identity. O The statement u, +0 # 0 + u, which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, + 0 U, which contradicts that O is an additive identity. O The statement u, + 0 + 0, which contradicts that u, must…