Let the vectors 2 + a + b i ^ + a + 2 b + c j ^ - b + c k ^ ,   1 + b i ^ + 2 b j ^ - b k ^ and 2 + b i ^ + 2 b j ^ + 1 - b k ^ ,   ∀ a , b , c ∈ R be co-planar. Then which of the following is true?

Question

Let the vectors 2 + a + b i ^ + a + 2 b + c j ^ - b + c k ^ , &#160; 1 + b i ^ + 2 b j ^ - b k ^ and 2 + b i ^ + 2 b j ^ + 1 - b k ^ , &#160; &#8704; a , b , c &#8712; R be co-planar. Then which of the following is true?

Aicharya · Accepted Answer

If the vectors are co-planar, a + b + 2 a + 2 b + c - b - c b + 1 2 b - b b + 2 2 b 1 - b = 0 Now R 1 &#8596; R 1 - R 2 , &#160; R 3 &#8596; R 3 - R 2 &#160; So a + 1 a + c - c b + 1 2 b - b 1 0 1 = 0 &#8658; ( a + 1 ) 2 b - ( a + c ) ( 2 b + 1 ) - c ( - 2 b ) = 0 &#8658; 2 a b + 2 b - 2 a b - a - 2 b c - c + 2 b c = 0 &#8658; 2 b - a - c = 0 &#8658; 2 b = a + c

Let the vectors 2 + a + b i ^ + a + 2 b + c j ^ - b + c k ^ ,   1 + b i ^ + 2 b j ^ - b k ^ and 2 + b i…

Solution

Let the vectors 2 + a + b i ^ + a + 2 b + c j ^ - b + c k ^ , &#160; 1 + b i ^ + 2 b j ^ - b k ^ and 2 + b i…

Solution

Let the vectors 2 + a + b i ^ + a + 2 b + c j ^ - b + c k ^ , 1 + b i ^ + 2 b j ^ - b k ^ and 2 + b i…