. (a) Let a and b be two non-zero vectors with a common
initial point 0 and whose directions are inclined at an angle O.
Define the vector product of a and b. (b) The position vectors of
the points A, B, C and D are 2i + j + 3k, 4i - j + 7k, -i - 2j - 2k
and 2i - 5j + k respectively. Show that the lines AB and CD are
skew. Find a direction...
Let vector B = 5.50 m at 60°. Let vector C have the same
magnitude as vector A and a direction angle greater than that of
vector A by 25°. Let vector A · vector B = 27.0 m2 and vector B ·
vector C = 34.5 m2. Find the magnitude and direction of vector
A.
Suppose that ac + bd = 0. Show that vectors [a, b] and [c, d]
are perpendicular. The number ac + bd is called the dot product of
the vectors [a, b] and [c, d].
A non-uniform b-spline curve knot vector is given as (-1, -1,
-1, -1/2, 0, 0, 0, 1, 1, 1, 3/2, 2, 2, 3, 3, 3, 3). Show the
equation diagrammatically and sketch the curve with their
respective control polygons if the curve is cubic (degree 3, order
4).
Verify using an example that vector a + (vector b * vector c) is
not equal to (vector a + vector b) * (vector a + vector c) explain
the problem that arrises