Let a = i + j + k , b = i - 3 j + 2 k and c = 3 i - 2 k . If a vector p satisfies the conditions p c = 0 and p a = b a , then the value of | p | = ...

Step-by-step solution

Given p a = b a ( p - b ) a = 0 p - b = a p = b + a Also given p c = 0 ( b + a ) c = 0 b c + ( a c ) = 0 Calculating the dot products: b c = ( i - 3 j + 2 k ) (3 i - 2 k ) = 3 - 4 = -1 a c = ( i + j + k ) (3 i - 2 k ) = 3 - 2 = 1 Substituting these values: -1 + (1) = 0 = 1 Therefore, p = b + a p = ( i - 3 j + 2 k ) + ( i + j + k ) = 2 i - 2 j + 3 k Magnitude of p : | p | = 2^2 + (-2)^2 + 3^2 = 4 + 4 + 9 = 17 Answer: 17