What will be the projection of vector A → = i ^ + j ^ + k ^ on vector B → = i ^ + j ^ ?

A cos θ B ^ = A A → · B → A B B ^ = A → · B → B B ^ = 2 2 i ^ + j ^ 2 = i ^ + j ^

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsMultiplication of vectorsEasy2 minPYQ_2021

PhysicsEasysingle choice

What will be the projection of vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ on vector $\vec{B} = \hat{i} + \hat{j} ?$

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Answer:

Solution:

$(A \cos θ) \hat{B} = A (\frac{\vec{A} \cdot \vec{B}}{A B}) \hat{B} = \frac{\vec{A} \cdot \vec{B}}{B} \hat{B}$
$= \frac{2}{\sqrt{2}} (\frac{\hat{i} + \hat{j}}{\sqrt{2}}) = \hat{i} + \hat{j}$

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: PYQ_2021

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