The magnitude of component of vector A = 3 i ^ + 4 j ^ along vector 2 i ^ + j ^ is α . Then find the value of 4 α 2 .

Component of A along B is A ⋅ B ^ . α = ∣ B ∣ A ⋅ B = 5 10 . Therefore, 4 α 2 = 4 ⋅ 5 100 = 5 .

Physics - Vectors Question with Solution | TestHub

PhysicsVectorsMultiplication of vectorsEasy2 minQB

PhysicsEasyinteger

The magnitude of component of vector $A = 3 \hat{i} + 4 \hat{j}$ along vector $2 \hat{i} + \hat{j}$ is $α$ . Then find the value of $\frac{α ^{2}}{4}$ .

Answer:

Solution:

Component of $A$ along $B$ is $A \cdot \hat{B}$ . $α = \frac{A \cdot B}{∣ B ∣} = \frac{10}{5}$ .

Therefore, $\frac{α ^{2}}{4} = \frac{100}{4 \cdot 5} = 5$ .

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: QB

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