Vector Properties

The shortest distance between two skew lines is computed using which expression involving their dire...

Two vectors of magnitudes 5 and 12 act at a point with an included angle of 90 degrees; evaluate the...

If the scalar triple product [a b c] equals 7 for three given vectors, what is the value of the rear...

Three unit vectors a, b and c satisfy a + b + c = 0; using this constraint, evaluate the sum a . b +...

For two vectors with magnitudes 4 and 3 enclosing a 30 degree angle, evaluate the sum of squares |a ...

Three vectors a = i + 2j + 3k, b = 2i + j + k and c = 3i + j + 2k are given; compute their scalar tr...

If two nonzero vectors a and b satisfy |a + b| = |a - b|, what can be concluded about the angle betw...

Consider the vectors a = 3i + 4j and b = i + 2j + 2k; find the scalar projection of vector a onto th...

What is the unit vector directed along the vector obtained by adding a = 2i - j + 2k and b = i + j -...

For what value of the scalar lambda are the three vectors i + j + k, i + lambda j + 2k and 2i + j + ...

The position vectors of three points are A(1,1,1), B(2,3,5) and C(3,5,1); find the area of triangle ...

Using the standard expansion identity, simplify the vector triple product a x (b x c) where a, b and...