a) Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1), B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).
b) For three vectors
a) The volume of the tetrahedron whose vertices are \( A = (3, 2, 1) \), \( ______ ___ _____ ________ ___ __________ ______ ______ __________ _________.
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________ ___ _______ _____ __________.
__________ ___ ______ _______ ___ __________ _________ ___ ______ ________ ____ ________.
___ __________ _______ _________ ___ _________ _______ _______.
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A metal sheet has, on the average, 5 defects per 10 sq. ft. Assuming a Poisson distribution, calculate the probability that a 15 sq. ft. piece of the metal sheet will have at least 4 defects
Using Stokes’ theorem evaluate where
and C is the circle
a) Obtain the derivative and the unit tangent vector for a vector function
b) For a scalar field where n is a non-zero real constant, show that
b) Determine the metric coefficients for the coordinate system (u,v,z) whose coordinates are related to the Cartesian coordinates by the following equations:
Is the system orthogonal?
a) Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1), B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).
b) For three vectors
The measurements of the bulk modulus of a material at different temperatures is as follows:
| 20 | 500 | 100 | 1200 | 1400 | 1500 | |
| K (G Pa) | 203 | 197 | 191 | 188 | 186 | 184 |
Out of 90 applicants for a job, 60 people get selected after the interview. If five applicants are selected at random, calculate the probability that 2 will get selected.