Let a → = i ^ + 2 j ^ - k ^ ,   b → = i ^ - j ^ and c → = i ^ - j ^ - k ^ be three given vectors. If r → is a vector such that r → × a → = c → × a → and r → · b → = 0 , then r → · a → is equal to

Question

Let a &#8594; = i ^ + 2 j ^ - k ^ , &#160; b &#8594; = i ^ - j ^ and c &#8594; = i ^ - j ^ - k ^ be three given vectors. If r &#8594; is a vector such that r &#8594; &#215; a &#8594; = c &#8594; &#215; a &#8594; and r &#8594; &#183; b &#8594; = 0 , then r &#8594; &#183; a &#8594; is equal to

Aicharya · Accepted Answer

r &#8594; - c &#8594; &#215; a &#8594; = 0 &#8658; &#160; r &#8594; = c &#8594; + &#955; a &#8594; taking dot product with b &#8594; Now, 0 = b &#8594; &#183; c &#8594; + &#955; a &#8594; &#183; b &#8594; &#8658; &#160; &#955; = - b &#8594; &#183; c &#8594; a &#8594; &#183; b &#8594; = - 2 - 1 = 2 So, r &#8594; &#183; a &#8594; = a &#8594; &#183; c &#8594; + 2 a &#8594; 2 = 0 + 2 &#215; 6 = 12

Let a → = i ^ + 2 j ^ - k ^ ,   b → = i ^ - j ^ and c → = i ^ - j ^ - k ^ be three…

Solution

Let a &#8594; = i ^ + 2 j ^ - k ^ , &#160; b &#8594; = i ^ - j ^ and c &#8594; = i ^ - j ^ - k ^ be three…

Solution

Let a → = i ^ + 2 j ^ - k ^ , b → = i ^ - j ^ and c → = i ^ - j ^ - k ^ be three…