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Mathematics in Physics

JEE Main level, single correct, medium

52 of 121

Question 52 of 121

Let $\vec{A}=\left(\hat{i}+\hat{j}\right)and\vec{B}=(2\hat{i}-\hat{j})$ . The magnitude of a coplanar vector $\vec{C}$ such that $\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B}$ is given by:

Show answer and solution

Answer: (C) $\sqrt{\dfrac{5}{9}}$

\vec{C}=a\hat{i}+b\hat{j}

then,

\vec{A}.\vec{C}=\vec{A}.\vec{B}

a+b=1.......(i)

\vec{B}.\vec{C}=\vec{A}.\vec{B}

2a-b=1......(ii)

solving equations

(i)

and

(ii)

we get,

a=\dfrac{1}{3},b=\dfrac{2}{3}

\left|\vec{C}\right|=\sqrt{\dfrac{1}{9}+\dfrac{4}{9}}=\sqrt{\dfrac{5}{9}}

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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More Physics practice

JEE Main Physics practice question on Mathematics in Physics (Multiplication of Vectors), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

Let A⃗=(i^+j^)andB⃗=(2i^−j^)\vec{A}=\left(\hat{i}+\hat{j}\right)and\vec{B}=(2\hat{i}-\hat{j})A=(i^+j^​)andB=(2i^−j^​) . The magnitude of a coplanar vector C⃗\vec{C}C such that A⃗.C⃗=B⃗.C⃗=A⃗.B⃗\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B}A.C=B.C=A.B is given by:

JEE Main question paper PDF

More Physics practice

Let $\vec{A}=\left(\hat{i}+\hat{j}\right)and\vec{B}=(2\hat{i}-\hat{j})$ . The magnitude of a coplanar vector $\vec{C}$ such that $\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B}$ is given by: