If a , b and c are mutually perpendicular vectors of the same magnitude, then the cosine of the angle between a and a + b + c is

Step-by-step solution

(b) Let | a |=| b |=| c |= Now, | a + b + c |^2=( a + b + c ) ( a + b + c ) aligned & =| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & = ^2+ ^2+ ^2+2(0+0+0)[ a b , b c , c a ] & =3 ^2 aligned | a + b + c |= 3 Now, let be angle between a and a + b + c aligned & = a ( a + b + c ) | a || a + b + c | = | a |^2 | a || a + b + c | & = ^2 + 3 = 1 3 . aligned