Let a, b,c, be vectors of length 3, 4, 5 respectively and $\mathbf{a}$ be perpendicular to $(\mathbf{b}+\mathbf{c}), \mathbf{b}$ to $(\mathbf{c}+\mathbf{a})$ and $\mathbf{c}$ to $(\mathbf{a}+\mathbf{b})$, then the value of $(\mathbf{a}+\mathbf{b}+\mathbf{c})$ is

JEE PHYSICS MCQ: MOTION IN PLANE

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Analyzing +4 | -1

Let a, b,c, be vectors of length 3, 4, 5 respectively and

\mathbf{a}

be perpendicular to

(\mathbf{b}+\mathbf{c}), \mathbf{b}

(\mathbf{c}+\mathbf{a})

and

\mathbf{c}

(\mathbf{a}+\mathbf{b})

, then the value of

(\mathbf{a}+\mathbf{b}+\mathbf{c})

View answer and explanation

Correct option: D

5 \sqrt{2}

The correct answer is D (

5 \sqrt{2}

) because by using the given perpendicularity conditions and vector algebra, we find the magnitude of the sum of the vectors.

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\mathrm{\vec P} = \mathrm{\vec A} + \mathrm{\vec B}\,\,\mathrm{and}\,P = A + B.

\mathrm{\vec A}\,and\,\mathrm{\vec B}

0^{\circ}

90^{\circ}

\mathrm{If}\,(\mathbf{a}+3 \mathbf{b}) \cdot(7 \mathbf{a}-5 \mathbf{b})=0

(\mathbf{a}-4 \mathbf{b}) \cdot(7 \mathbf{a}-2 \mathbf{b})=0

\mathbf{a}

\mathbf{b}

\theta

\left(90^{\circ}-\theta\right)

39.2 \mathrm{~ms}^{-1}

50 \mathrm{~m}

{g}=9.8 \mathrm{~ms}^{-2}