NEET UG PHYSICS MCQ: MOTION IN PLANE

1 Hard

1 of 1

Application +4 | -1

Consider three vectors

\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}

and

\mathbf{C}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}

. A vector

\mathbf{X}

of the form

\alpha \mathbf{A}+\beta \mathbf{B}

(

\alpha

and

\beta

are numbers) is perpendicular to

\mathbf{C}

. The ratio of

\alpha

and

\beta

View answer and explanation

Correct option: A

1: 1

Option A (

1: 1

) is correct because the condition of perpendicularity between vector X and C leads to the equation

\alpha = \beta

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\mathrm{\vec a}\,and\,\mathrm{\vec b}

\mathrm{\vec a}\,and\,\mathrm{\vec b}

\overrightarrow P \,\,.\,\,\overrightarrow Q = 0\,and\,\overrightarrow P \,\, \times \,\,\overrightarrow Q = 0

\overrightarrow Q \,and\,\overrightarrow R

\vec{A}=3 \hat{i}+4 \hat{j}

\vec{B}=6 \hat{i}+8 \hat{j}

A

B

\overrightarrow{\mathrm{A}}

\overrightarrow{\mathrm{B}}

{\cot ^{ - 1}}\left( 2 \right)