Basic Mathematics & Vectors

Three forces of magnitude 6 N, 8 N, and 10 N keep a particle in equilibrium. Find the angle between the 6 N and 8 N forces.

Vectors A = 5î − 2ĵ, B = −3î + 4ĵ, and C satisfy A + B + C = 0. Find C.

Find dy/dx at x = 1 for y = x²/(x+1).

Evaluate ∫(2x + 3) dx from x = 1 to x = 4.

Find the angle between vectors A = î and B = î + ĵ.

Find the area of the parallelogram formed by vectors A = 3î and B = 4ĵ.

Find the magnitude of the resultant of three vectors A = 2î+3ĵ, B = −î+4ĵ, C = 3î−5ĵ.

Vectors a = î, b = î+ĵ, c = î+ĵ+k̂. Find the scalar triple product a·(b×c).

Find the maximum value of y = −x² + 4x + 1.

Find the projection (component) of vector A = 5î along the direction of B = 3î + 4ĵ.

Find the area under the curve y = x² between x = 0 and x = 3.

A force of 10 N acts at 60° to a given direction. Find its component along that direction.