Let three vectors a → , b → and c → be such that c → is coplanar with a → and b → , a → · c → = 7 and b → is perpendicular to c → , where a → = - i ^ + j ^ + k ^ and b → = 2 i ^ + k ^ , then the value of 2 a → + b…

Question

Let three vectors a &#8594; , b &#8594; and c &#8594; be such that c &#8594; is coplanar with a &#8594; and b &#8594; , a &#8594; &#183; c &#8594; = 7 and b &#8594; is perpendicular to c &#8594; , where a &#8594; = - i ^ + j ^ + k ^ and b &#8594; = 2 i ^ + k ^ , then the value of 2 a &#8594; + b &#8594; + c &#8594; 2 is

Aicharya · Accepted Answer

Let c &#8594; = &#955; b &#8594; &#215; a &#8594; &#215; b &#8594; = &#955; b &#8594; &#183; b &#8594; a &#8594; - b &#8594; &#183; a &#8594; b &#8594; = &#955; 5 - i ^ + j ^ + k ^ + 2 i ^ + k ^ = &#955; - 3 i ^ + 5 j ^ + 6 k ^ c &#8594; &#183; a &#8594; = 7 &#8658; 3 &#955; + 5 &#955; + 6 &#955; = 7 &#955; = 1 2 &#8756; &#160; 2 - 3 2 - 1 + 2 i ^ + 5 2 + 1 j ^ + 3 + 1 + 1 k ^ 2 = 2 1 4 + 49 4 + 25 = 25 + 50 = 75

Let three vectors a → , b → and c → be such that c → is coplanar with a → and…

Solution

Let three vectors a &#8594; , b &#8594; and c &#8594; be such that c &#8594; is coplanar with a &#8594; and…

Solution

Let three vectors a → , b → and c → be such that c → is coplanar with a → and…