For the given vector, show that |𝐏|^2=𝑚^2+𝑛^2+𝑚𝑛+3/4𝑞^2 .

Question

A vector 𝐏 is given by 𝐏=𝑚𝐚+𝑛𝐛+𝑞(𝐚×𝐛), where 𝐚 and 𝐛 are unit vectors inclined to each other at an angle of 60 degree.

(a) Show that |𝐏|2=𝑚²+𝑛²+𝑚𝑛+3/4 𝑞².

(b) Express 𝐏.𝐚 and 𝐏.𝐛 in terms of m, n, q.

(c) Find two sets of values for m, n, q such that  𝐏 is a unit vector at right angles to 𝐚  and making an angle of 45 degree with 𝐛  .

Answer 1

|𝐏|=(𝑚^2+𝑛^2+𝑚𝑛+3/4𝑞^2)^.5