Q24 of 25 Page 10

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are .

To prove: the direction cosines of a vector are


Explanation: Let the required vector


And, the direction cosines are x,y and c


Since, the vector is equally inclined to axes OX, OY and OZ; then the direction cosines are equal




The vector is


And,





SO, The direction cosines are


Can be written as




Hence, Proved


More from this chapter

All 25 →
21

For any two vectors and , prove that and hence show that (a1b1 + a2b2 + a3b3)2 ≤ (a12 + a22 + a32)(b12 + b22 + b32).

 22

If are three vectors such that and , find the angle between and .

 23

Prove that in a ΔABC, , where a, b, and c are the magnitude of sides of the triangle opposite to angles A, B and C respectively.

 25

If and are two-unit vectors inclined at an angle θ, then prove that

(i)


(ii)