Null vectors Questions

The position vectors of the vertices A, B, C and D of a quadrilateral ABCD are given by

3î + 4ĵ − 2k̂,

4î − 4ĵ − 3k̂,

2î − 3ĵ + 2k̂

and

6î − 2ĵ + k̂

respectively. What is the angle between the diagonals AC and BD of the quadrilateral?

What is the area of the parallelogram whose sides are represented by the vectors

î + 2ĵ + 3k̂

and

2î + ĵ + 2k̂ ?

How many of the following can be a vector perpendicular to both the vectors

2î − ĵ + k̂

and

î + ĵ + 3k̂ ?

I. 4î − 5ĵ − 3k̂

II. −8î − 10ĵ + 6k̂

III. (1/50)(−4î − 5ĵ + 3k̂)

Select the correct answer.

Let a b, and (a× b)   be unit vectors. What is (a.b)  equal to?

The position vectors of three points A, B and C are a b, and c, respectively, such that What is AB: BC equal to?

Which of the statements given above is/are correct?

then what is a b. equal to?