Let c → be a vector perpendicular to the vectors a → = i ^ + j ^ - k ^ and b → = i ^ + 2 j ^ + k ^ . If c → · ( i ^ + j ^ + 3 k ^ ) = 8 , then the value of c → · ( a → × b → ) is equal to

Question

Let c &#8594; be a vector perpendicular to the vectors a &#8594; = i ^ + j ^ - k ^ and b &#8594; = i ^ + 2 j ^ + k ^ . If c &#8594; &#183; ( i ^ + j ^ + 3 k ^ ) = 8 , then the value of c &#8594; &#183; ( a &#8594; &#215; b &#8594; ) is equal to

Aicharya · Accepted Answer

c &#8594; = &#955; ( a &#8594; &#215; b &#8594; ) a &#8594; &#215; b &#8594; = i ^ j ^ k ^ 1 1 - 1 1 2 1 ( a &#8594; &#215; b &#8594; ) = 3 i ^ - 2 j ^ + k ^ c &#8594; &#183; ( i ^ + j ^ + 3 k ^ ) = &#955; ( 3 i ^ - 2 j ^ + k ^ ) &#183; ( i ^ + j ^ + 3 k ^ ) &#8658; &#955; ( 4 ) = 8 &#8658; &#955; = 2 c &#8594; = 2 ( a &#8594; &#215; b &#8594; ) Hence, c &#8594; &#183; ( a &#8594; &#215; b &#8594; ) = 28

Let c → be a vector perpendicular to the vectors a → = i ^ + j ^ - k ^ and b → = i ^ + 2 j…

Solution

Let c &#8594; be a vector perpendicular to the vectors a &#8594; = i ^ + j ^ - k ^ and b &#8594; = i ^ + 2 j…

Solution

Let c → be a vector perpendicular to the vectors a → = i ^ + j ^ - k ^ and b → = i ^ + 2 j…