Question

If the vectors A = 21+ 2+xk and = 21+2)• ure perpendicular to each other, then the
of x is
b​

Answer 1

Correct Question :-

◉ If the vectors A = 2i + 2j + xk and B = 2i + 2j + k are perpendicular to each other. Find the value of x

Answer :-

We know, for two perpendicular vectors A and B, the dot product of A and B is 0.

Comparing the two vectors with the standard form of a vector i.e., a₁i + b₁j + c₁k , we have for the two vectors:

• a₁ = 2 , b₁ = 2 , c₁ = x
• a₂ = 2 , b₂ = 2 , c₂ = 1

We know, Dot product of two vectors is given by the following formulae:

⇒ A . B = a₁a₂ + b₁b₂ + c₁c₂

⇒ 0 = 2×2 + 2×2 + 1×x

⇒ 0 = 4 + 4 + x

⇒ x = -8

Value of x is -8

Note :-

It is unclear in the question regarding the actual value of the k component of the vector B. So I am assumed it to be 1 , If it is not 1 , let it be ɑ , then the value of x would be -8/ɑ

Some Information :-

☛ For any two vectors A and B which are perpendicular to each other, The cross product of A and B would be 1 u {u is unit vector } while dot product would be 0.

☛ Cross Product is a type of multiplication of vectors which results in a vector instead of a number. Denoted by A × B.

Dot Product is a type of multiplication of vectors in which the result we get is just a number. Denoted by A . B