Let ₁ be the plane determined by the vectors i + j and j + k , ₂ be the plane determined by the vectors i - j and i + j - k . Let a be a vector parallel to the line of intersection of ₁ and ₂ . If | a |= 14 , then | a ( i + j + k )|=

Step-by-step solution

For ₁: n ₁= | array ccc i & j & k 1 & 1 & 0 0 & 1 & 1 array |= i - j + k For ₂: n ₂= | array ccc i & j & k 1 & -1 & 0 1 & 1 & -1 array |= i + j +2 k For line : b = n ₁ n ₂= | array ccc i & j & k 1 & -1 & 1 1 & 1 & 2 array |=-3 i - j +2 k a = (3 i + j -2 k )| a |= 9 ^2+ ^2+4 ^2 = 14 ^2=1 = 1 Now, | a ( i + j + k )|=| 1(3 i + j -2 k ) ( i + j + k )|=2