Ex 10.4, 3 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.4, 3 If a unit vector makes angles 3 with , 4 , with and an acute angle with , then find and hence, the components of . Let us take a unit vector = + y + z So, magnitude of = = 1 Also, Angle of with = . = cos (x + y + z ). (0 + .0 + 1 ) = 1 1 cos (x 0) + (y 0) + (z 1) = cos 0 + 0 + z = cos z = cos Now, Magnitude of = 2+ 2+ 2 1 = 1 2 2 + 1 2 2 + 2 1 = 1 4 + 1 2 + 2 1 = 3 4 + 2 3 4 + 2 = 1 3 4 + 2 2 = 12 3 4 + 2 = 1 2 = 1 3 4 2 = 1 4 cos = 1 4 cos = 1 2 Since is given an acute angle So, < 90 is in 1st quadrant & cos is positive in 1st quadrant So, cos = + 1 2 = 60 = Also, z = cos = cos 60 = Hence x = 1 2 , y = 1 2 & z = 1 2 The required vector is 1 2 + 1 2 + 1 2 So, components of are , &