Find the distance from the vertex of the right-circular cone to the centroid of its volume. Answer: Z = i IN H h
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- Dot Product, rectangular coordinates: If A = 5 i + -8 j and B = 12 i + 18 j, find A-BA closed water tank has the form of a cuboid with a square base with sides of length x and a height h. The total surface area of the tank is 16000 cm2 Find the value of x which maximises the volume. Give your answer correct to 2 decimal places.What is the direction of the vector product A × B? Use the legend in the box to indicate direction. a В (out) (out) O (in) zero in C b zero a e h out
- Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular to plane PQR . P(-1,1,0), Q(0,0,1), R(0,0, – 1)Evaluate the cross product A×B if A = 27, B = 85 and θ = 101°. Evaluate the cross product C×D if C = 16 and D = 43.Three vectors are given as: A = 3â – 9âỹ B = 7ââ + 10ŷ C = 4⣠+ 5ÿ+ 62 These three vectors are used to define a parallelepiped. (a) What is the volume of the parallelepiped? (b) What is the surface area of the parallelepiped?
- . Calculate the area of the parallelogram whose two adjacent sides are formed by the vectors. A = 31 + 4k B = 23+k.Two vectors %3D 2 and B = 2 + 3 . Find the approximate angle between the vectors (-3 A ) and (2 )? .A None .B 30° .C 60°Consider two vectors A and B such that Ã × B – B (÷ B Find the angle between A and B if ß = 6. O Report your numerical answer below, assuming three significant figures.