Find the value of 4Sinh πi/3.

Find the A dot B if /A/ and /B/ are 26 and 17 respectively and the angle between them is π/3.

Find the work done in moving an object along straight line from (3,2,-1) to (2,-1,4) in a force field given by F = 4i – 3j + 2k.

Find the acute angle formed by two diagonals of a cube.

Find the projection of vector 2i – 3j + 6k on the vector i + 2j + 2k.

Find the area of the parallelogram with diagonals represented by vectors A = 3i + j – 2k and B = i – 3j + 4k.

Find the volume of the parallelepiped whose edges are represented by A = 2i – 3j + 4k, B = i + 2j – k and C = 3i – j + 2k.

For what values of a are A = ai – 2j + k and B = 2ai + aj – 4k perpendicular?

A particle moves along the curve whose parametric equation is x = e^-t, y = 2Cos3t, z = 2Sin3t where t is the time. Find the magnitude of the velocity at t = 0.

A particle moves along the curve whose parametric equation is x = e^-t, y = 2Cos3t, z = 2Sin3t where t is the time. Find the magnitude of acceleration at t = 0.

The cross product of A = 4i + 2j with B is zero when the dot product of A and B is 30. Find B.

Given the vector A = 2i - 4j + k, B = i + j – 3k, C = -i + 2j + 2k, find (AxB) ● (C x A)

Solve for a such that the 3 vectors 2i – j + k, 1 + 2j – 3k and 3i + aj + 5k are coplanar vectors.

Find the volume of a parallelopiped with sides are A = 3i – j, B = j + 2k, C = i + 5j + 4k.

Find the projection of A = 10i – 2j + 8k in the direction of B = 2i – 6j + 3k.

Find a so that 2i – 3j + 5k and 3i + aj – 2k are perpendicular.

Compute the angle which the position vector 3i – 6j + 2k makes with the y-axis.

Solve for the magnitude of a force which must be added to the following two vectors forces 2i – 7k and 3j + 2k to give a resultant of 7i – 6j – k (all are in Newton).

Find the area of the area of the parallelogram with adjacent sides represented by i – 2j + 3k and 2i + j + 4k.

Given are A = i – 2j+3k and B = 3i + j+2k. Find the unit vector perpendicular to both A and B.

Find the divergence of the vector field.

If A = xz² i + 2yj – 3xzk and B = 3xzi + 2yzj – z ²k, find A x ( ∇ x B) at the point (1, -1, 2).

Find a unit vector which is perpendicular to the surface of the paraboloid of revolution z = x² + y² at the pt (1,2,5)

Evaluate ∇ ● (/r/ ³ r) if r = xi + yj + 2k and /r/ = sq.rt of (x^2 + y^2 + z^2)

Find the directional derivative of P = 4e raised to (2x – y + z) at the pt (1,1,-1) in the direction towards the pt (-3,5,6)

For what value of a will the vector A = (axy – z^3)i + (a – 2) x^2 j + (1 – a) xz^2k have curl identically equal to zero.

Find the work done in moving an object along a vector a = 3i+4j if the force applied is b = 2i+j.

Write the vector of length 2 and direction 150 degrees in the form ai + bj.

Given the vector V = i + 2j + k, what is the angle between V and the x- axis?

Find the area of the first octant part of the plane (x/a) + (y/b) + (z/c) = 1, where a, b and c are positive.

If z₁ = 3 – 4i and z₂ = -4 + 3i find z₁ * z₂.