Assertion (A): For two non-zero vectors \overrightarrow{a} ...

CBSE Class 12 Math 2024 All Sets Solved Paper

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Assertion (A): For two non-zero vectors

{a}↖{→}

and

{b}↖{→}

{a}↖{→}.{b}↖{→} = {b}↖{→}.{a}↖{→}

.
Reason (R): For two non-zero vectors

{a}↖{→}

and

{b}↖{→}

{a}↖{→}× {b}↖{→} = {b}↖{→}×{a}↖{→}

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.

Solution:

The scaler or dot product is commutative i.e.

{a}↖{→} . {b}↖{→} ={b}↖{→}. {a}↖{→}

, so Assertion (A) is true.
But vector product is not commutative i.e.

{a}↖{→}×{b}↖{→} \ne {b}↖{→} × {a}↖{→}

, so Reason (R) is false.

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