Let α   ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ ,    b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = { α : a → , b → and c → are coplanar}

Question

Let &#945; &#8201; &#8712; R and the three vectors a &#8594; = &#945; i ^ + j ^ + 3 k ^ , &#8201;&#8201; b &#8594; = 2 i ^ + j ^ - &#945; k ^ and c &#8594; = &#945; i ^ - 2 j ^ + 3 k ^ . Then the set S = { &#945; : a &#8594; , b &#8594; and c &#8594; are coplanar}

Aicharya · Accepted Answer

If a &#8594; , &#160; b &#8594; &#160; and &#160; c &#8594; are coplanar then, &#945; 1 3 2 1 - &#945; &#945; - 2 3 = 0 &#8658; 3 &#945; 2 + 18 = 0 &#8658; &#945; &#8712; &#981;

Let α   ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ ,    b…

Solution

Let &#945; &#8201; &#8712; R and the three vectors a &#8594; = &#945; i ^ + j ^ + 3 k ^ , &#8201;&#8201; b…

Solution

Let α ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ , b…