If a = i -2 j +3 k and b =2 i +3 j - k , then the angle between the vectors (2 a + b ) and ( a +2 b ) is

Step-by-step solution

aligned & Given, 2 a + b =4 i - j +5 k & a +2 ~b =5 i +4 j + k & |2 a + b |= (4)^2+(-1)^2+(5)^2 = 42 & | a +2 ~b |= 5^2+4^2+1^2 = 42 aligned Angle between (2 a + b ) and ( a +2 b ) is given by aligned & = (2 a + b )( a +2 b ) |2 a + b || a +2 b | & = (4 i - j +5 k )(5 i +4 j + k ) 42 42 = 21 42 & = 1 2 & = 3 aligned