Define the vector product of two vectors ` vec (a) and vec (b) ` . Give geometrical interpretation of ` vec (a) xx vec (b)` . Show that the satisfies the distributive law .

For any two vectors vec(a) " and " vec(b) which of the following is true?

Two vectors vec(a) and vec (b) are such that |vec(a).vec(b)| = |vec(a) xx vec(b)| , then find the angle between the vectors vec(a) and vec(b) .

Find |vec(a)-vec(b)| , if two vectors vec(a) and vec(b) are such that |vec(a)| = 2 , |vec(b)| = 3 and vec (a) . vec (b) = 4

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

For any two vectors vec(a) and vec(b) , show that | vec (a).vec(b)| le |vec(a)||vec(b)|

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|vecb|

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

If vector vec a+ vec b bisects the angle between vec a and vec b , then prove that | vec a| = | vec b| .

If the vector product of a constant vector vec O A with a variable vector vec O B in a fixed plane O A B be a constant vector, then the locus of B is a. a straight line perpendicular to vec O A b. a circle with centre O and radius equal to | vec O A| c. a straight line parallel to vec O A d. none of these