If A = 5 i ^ + 2 j ^ and B = a i ^ + 3 j ^ are perpendicular to each other, the value of 'a' is

For two vectors to be perpendicular, their dot product must be zero. A ⋅ B = 0 ( 5 i ^ + 2 j ^ ) ⋅ ( a i ^ + 3 j ^ ) = 0 5 a + 2 ( 3 ) = 0 5 a + 6 = 0 a = 5 − 6 Answer: 5 − 6

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsMultiplication of vectorsEasy2 minPYQ_2026

PhysicsEasysingle choice

If $A = 5 \hat{i} + 2 \hat{j}$ and $B = a \hat{i} + 3 \hat{j}$ are perpendicular to each other, the value of 'a' is

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Solution:

For two vectors to be perpendicular, their dot product must be zero.

$A \cdot B = 0$

$(5 \hat{i} + 2 \hat{j}) \cdot (a \hat{i} + 3 \hat{j}) = 0$

$5 a + 2 (3) = 0$

$5 a + 6 = 0$

$a = \frac{- 6}{5}$

Answer: $\frac{- 6}{5}$

Stream:MHT_CETSubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: PYQ_2026

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