Assertion- If dot product and cross product of A and B are zero- it implies that one of the vector A and B must be null vector-Reason- Null vector is a vector with zero magnitude-

A . nbsp;B = |A||B| cosθ = 0 A×B = |A||B| sinθ = 0 If A and nbsp;B are not null vectors, then both sinθ and cosθ cannot be zero simultaneously, so it is ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Physics

Multiplication with Vectors

Assertion: If...

Question

Assertion: If dot product and cross product of $\to A$ and $\to B$ are zero, it implies that one of the vector $\to A$ and $\to B$ must be null vector.
Reason: Null vector is a vector with zero magnitude.

If both assertion and reason are true and the reason is the correct explanation of the assertion.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

If both assertion and reason are true but reason is not the correct explanation of the assertion.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

If assertion is true but reason is false.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

If the assertion and reason both are false.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

If assertion is false but reason is true.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B If both assertion and reason are true but reason is not the correct explanation of the assertion.
$\to A . \to B = | \to A | | \to B | cos θ = 0$
$\to A \times \to B = | \to A | | \to B | sin θ = 0$

If $\to A$ and $\to B$ are not null vectors, then both $sin θ$ and $cos θ$ cannot be zero simultaneously, so it is essential that one of the vector must be null vector.

Suggest Corrections

Similar questions

Assertion : If dot product and cross product of vector A and vector B are zero, it implies that one of the vector A and B must be a null vector.

Reason : Null vector is a vector with zero magnitude.

Q. Statement 1: If dot product and cross product of

\to A

and

\to B

are zero, it implies that one of the vector

\to A

and

\to B

must be a null vector.
Statement 2: Null vector is a vector with zero magnitude.

Q. Assertion: If dot product and cross product of

\to A

and

\to B

are zero, it implies that one of the vector

\to A

and

\to B

must be null vector.
Reason: Null vector is a vector with zero magnitude.

Q. Assertion(A) : A null vector is a vector whose magnitude is zero and direction is arbitrary
Reason(R) : A null vector does not exist

Q. Assertion :Statement-I : If the initial and final positions coincide, the displacement is a null vector.
Because Reason: Statement-II : A physical quantity can not be called a vector, if its magnitude is zero.

Join BYJU'S Learning Program

Assertion: If dot product and cross product of →A and →B are zero, it implies that one of the vector →A and →B must be null vector. Reason: Null vector is a vector with zero magnitude.

Assertion: If dot product and cross product of $\to A$ and $\to B$ are zero, it implies that one of the vector $\to A$ and $\to B$ must be null vector.
Reason: Null vector is a vector with zero magnitude.