Let a → = i ^ + j ^ + k ^ , b → and c → = j ^ - k ^ be three vectors such that a → × b → = c → and a → · b → = 1 . If the length of projection vector of the vector b → on the vector a → × c → is l , then the value of…

Question

Let a &#8594; = i ^ + j ^ + k ^ , b &#8594; and c &#8594; = j ^ - k ^ be three vectors such that a &#8594; &#215; b &#8594; = c &#8594; and a &#8594; &#183; b &#8594; = 1 . If the length of projection vector of the vector b &#8594; on the vector a &#8594; &#215; c &#8594; is l , then the value of 3 l 2 is equal to _____.

Aicharya · Accepted Answer

Given, a &#8594; &#215; b &#8594; = c &#8594; &#8658; a &#8594; &#215; b &#8594; &#183; c &#8594; = c &#8594; 2 = 1 2 + 1 2 2 = 2 Here, a &#8594; &#215; c &#8594; = i ^ j ^ k ^ 1 1 1 0 1 - 1 = - 2 i ^ + j ^ + k ^ Projection of b &#8594; on a &#8594; &#215; c &#8594; = &#8467; &#8658; b &#8594; &#183; a &#8594; &#215; c &#8594; a &#8594; &#215; c &#8594; = &#8467; &#8658; a &#8594; &#215; b &#8594; &#183; c &#8594; 2 2 + 1 + 1 = &#8467; &#8756; &#160; &#8467; = 2 6 &#8658; &#8467; 2 = 4 6 So, 3 &#8467; 2 = 2

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

Solution

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

Solution

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