A vector r of magnitude 3 2 units which makes angles of 4 and 2 respectively with Y and Z axes is

Step-by-step solution

Let the direction cosines of the vector r be l, m, n . Given that the vector makes angles of 4 and 2 with the Y and Z axes respectively, we have: m = ( 4 ) = 1 2 n = ( 2 ) = 0 Using the relation l^2 + m^2 + n^2 = 1 : l^2 + ( 1 2 )^2 + 0^2 = 1 l^2 + 1 2 = 1 l^2 = 1 2 l = 1 2 The vector r is given by: r = | r |(l i + m j + n k ) Substituting the given magnitude | r | = 3 2 and the direction cosines: r = 3 2 ( 1 2 i + 1 2 j + 0 k ) r = 3 i + 3 j Answer: r = 3 i + 3 j