Let a → = i ^ + α j ^ + 3 k ^ and b → = 3 i ^ - α j ^ + k ^ . If the area of the parallelogram whose adjacent sides are represented by the vectors a → and b → is 8 3 square units, then a → · b → is equal to ___ .

Question

Let a &#8594; = i ^ + &#945; j ^ + 3 k ^ and b &#8594; = 3 i ^ - &#945; j ^ + k ^ . If the area of the parallelogram whose adjacent sides are represented by the vectors a &#8594; and b &#8594; is 8 3 square units, then a &#8594; &#183; b &#8594; is equal to ___ .

Aicharya · Accepted Answer

a &#8594; = i ^ + &#945; j ^ + 3 k ^ b &#8594; = 3 i ^ - &#945; j ^ + k ^ area of parallelogram = | a &#8594; &#215; b &#8594; | = 8 3 . a &#8594; &#215; b &#8594; = i ^ j ^ k ^ 1 &#945; 3 3 - &#945; 1 = i ^ 4 &#945; - j ^ - 8 + k ^ - 4 &#945; &#8756; | a &#8594; &#215; b &#8594; | = 64 + 32 &#945; 2 = 8 3 &#8658; 2 + &#945; 2 = 6 &#8658; &#945; 2 = 4 &#8756; a &#8594; &#183; b &#8594; = 3 - &#945; 2 + 3 = 2

Let a → = i ^ + α j ^ + 3 k ^ and b → = 3 i ^ - α j ^ + k ^ . If the area of the…

Solution

Let a &#8594; = i ^ + &#945; j ^ + 3 k ^ and b &#8594; = 3 i ^ - &#945; j ^ + k ^ . If the area of the…

Solution

Let a → = i ^ + α j ^ + 3 k ^ and b → = 3 i ^ - α j ^ + k ^ . If the area of the…