Vectors vecA , vecB and vecC are such that vecA ⋅ vecB = 0 and vecA ⋅ vecC = 0 . Then the vector parallel to vecA is

Question

Vectors vecA , vecB and vecC are such that vecA ⋅ vecB = 0 and vecA ⋅ vecC = 0 . Then the vector parallel to vecA is (A)  vecA × vecB  (B)  vecB + vecC  (C)  vecB × vecC  (D)  vecB and vecC

Tardigrade Admin · Accepted Answer

Vector triple product of three vectors A , B and C is A × ( B × C) = ( A ⋅ C) B - ( A ⋅ B) C Given: A ⋅ B = 0, A ⋅ C = 0 ∴ A × ( B × C) Thus the vector A is parallel to vector B × C .

Q. Vectors $A, B$ and $C$ are such that $A \cdot B = 0$ and $A \cdot C = 0$ .
Then the vector parallel to $A$ is

$A \times B$

$B + C$

$B \times C$

$B$ and $C$

Vector triple product of three vectors $A, B$ and $C$ is
$A \times (B \times C) = (A \cdot C) B - (A \cdot B) C$
Given : $A \cdot B = 0, A \cdot C = 0$
$∴ A \times (B \times C)$
Thus the vector $A$ is parallel to vector $B \times C$ .

Q. Vectors A,B and C are such that A⋅B=0 and A⋅C=0 . Then the vector parallel to A is

A×B

B+C

B×C

B and C