The cosine of the angle included between the lines r =(2 + -2 k )+ ( -2 -2 k ) and r =( + +3 k )+ (3 +2 -6 k ) where , R is

Step-by-step solution

(D) ⁻¹ ( 1 3 )+ ⁻¹ ( 1 5 )= ⁻¹ ( 1 3 + 1 5 1- 1 3 1 5 )= ⁻¹ ( 8 15 15-1 15 )= ⁻¹ ( 8 14 )= ⁻¹ ( 4 7 ) ⁻¹ ( 1 7 )+ ⁻¹ ( 1 8 )= ⁻¹ ( 1 7 + 1 8 1- 1 7 1 8 )= ⁻¹ ( 15 56 55 56 )= ⁻¹ ( 15 55 )= ⁻¹ ( 3 11 ) Now, aligned ⁻¹ ( 4 7 )+ ⁻¹ ( 3 11 ) &= ⁻¹ ( 4 7 + 3 11 1- 4 7 3 11 )= ⁻¹ ( 44+21 77 77-12 77 )= ⁻¹ ( 65 77 65 77 ) &= ⁻¹(1)= 4 aligned