Let a → = 2 i ^ - 3 j ^ + 4 k ^ and b → = 7 i ^ + j ^ - 6 k ^ If r → × a → = r → × b → , r → · ( i ^ + 2 j ^ + k ^ ) = - 3 , then r → · ( 2 i ^ - 3 j ^ + k ^ ) is equal to:

Question

Let a &#8594; = 2 i ^ - 3 j ^ + 4 k ^ and b &#8594; = 7 i ^ + j ^ - 6 k ^ If r &#8594; &#215; a &#8594; = r &#8594; &#215; b &#8594; , r &#8594; &#183; ( i ^ + 2 j ^ + k ^ ) = - 3 , then r &#8594; &#183; ( 2 i ^ - 3 j ^ + k ^ ) is equal to:

Aicharya · Accepted Answer

r &#8594; &#215; a &#8594; - r &#8594; &#215; b &#8594; = 0 &#8658; r &#8594; &#215; a &#8594; - b &#8594; = 0 &#8658; r &#8594; = &#955; a &#8594; - b &#8594; &#8658; r &#8594; = &#955; - 5 i ^ - 4 j ^ + 10 k ^ Also r &#8594; &#183; i ^ + 2 j ^ + k ^ = - 3 &#8658; &#955; - 5 - 8 + 10 = - 3 &#955; = 1 Now r &#8594; = - 5 i ^ - 4 j ^ + 10 k ^ = r &#8594; &#183; 2 i ^ - 3 j ^ + k ^ = - 10 + 12 + 10 = 12

Let a → = 2 i ^ - 3 j ^ + 4 k ^ and b → = 7 i ^ + j ^ - 6 k ^ If r → × a → = r…

Solution

Let a &#8594; = 2 i ^ - 3 j ^ + 4 k ^ and b &#8594; = 7 i ^ + j ^ - 6 k ^ If r &#8594; &#215; a &#8594; = r…

Solution

Let a → = 2 i ^ - 3 j ^ + 4 k ^ and b → = 7 i ^ + j ^ - 6 k ^ If r → × a → = r…