QJEEM20Mac745: JEE Main 2020 Physics - Class 11 JEEM20Mac745 Solution: If and be two non-zero vectors such that and is perpendicular…

Question

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If

\overrightarrow x

and

\overrightarrow y

be two non-zero vectors such that

\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|

and

{2\overrightarrow x + \lambda \overrightarrow y }

is perpendicular to

{\overrightarrow y }

, then the value of

\lambda

is _________ .

Accepted Answer

\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|

Squaring both sides we get

{\left| {\overrightarrow x } \right|^2} + 2\overrightarrow x .\overrightarrow y + {\left| {\overrightarrow y } \right|^2} = {\left| {\overrightarrow x } \right|^2}

\Rightarrow

2\overrightarrow x .\overrightarrow y + \overrightarrow y .\overrightarrow y

= 0 ....(1)

Given

{2\overrightarrow x + \lambda \overrightarrow y }

is perpendicular to

{\overrightarrow y }

\therefore

\left( {2\overrightarrow x + \lambda \overrightarrow y } \right).\overrightarrow y

= 0

\Rightarrow

2\overrightarrow x .\overrightarrow y + \lambda \overrightarrow y .\overrightarrow y

= 0 ....(2)

Comparing (1) & (2) we get,

\lambda

= 1

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