Let u → be a vector coplanar with the vectors a → = 2 i ^ + 3 j ^ - k ^ and b → =   j ^ + k ^ . If u → is perpendicular to a → and u → ⋅ b → = 24 , then u → 2 is equal to:

Question

Let u &#8594; be a vector coplanar with the vectors a &#8594; = 2 i ^ + 3 j ^ - k ^ and b &#8594; = &#160; j ^ + k ^ . If u &#8594; is perpendicular to a &#8594; and u &#8594; &#8901; b &#8594; = 24 , then u &#8594; 2 is equal to:

Aicharya · Accepted Answer

As u &#8594; = &#955; [ a &#8594; &#215; ( a &#8594; &#215; b &#8594; ) ] u &#8594; = &#955; [ [ a &#8594; . b &#8594; ] a &#8594; &#8722; | a &#8594; | 2 b &#8594; ] u &#8594; = &#955; [ 2 a &#8594; &#8722; 14 b &#8594; ] u &#8594; . b &#8594; = 2 &#955; [ a &#8594; . &#8201; b &#8594; &#8722; 7 | b &#8594; | 2 ] = 2 &#955; [ 2 &#8722; 14 ] 24 = &#8722; 24 &#955; &#955; = &#8722; 1 u &#8594; = 14 b &#8594; &#8722; 2 a &#8594; u &#8594; = - 4 i ^ + 8 j ^ + 16 k ^ | u &#8594; | 2 = 4 2 + 8 2 + 16 2 = 336

Let u → be a vector coplanar with the vectors a → = 2 i ^ + 3 j ^ - k ^ and b → =   j…

Solution

Let u &#8594; be a vector coplanar with the vectors a &#8594; = 2 i ^ + 3 j ^ - k ^ and b &#8594; = &#160; j…

Solution

Let u → be a vector coplanar with the vectors a → = 2 i ^ + 3 j ^ - k ^ and b → = j…