QJEEM21Ma0789: JEE Main 2021 Physics - Class 11 JEEM21Ma0789 Solution: In a triangle ABC, if , then the projection of the vector on is …

Question

Verified Solution • 2025–26 Session moderate

In a triangle ABC, if

|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10

, then the projection of the vector

\overrightarrow {AB}

on

\overrightarrow {AC}

is equal to :

Accepted Answer

|\overrightarrow a | = 8,|\overrightarrow b | = 7,|\overrightarrow c | = 10

Projection of

\overrightarrow {AB}

on

\overrightarrow {AC}

=

|\overrightarrow {AB} |cos\theta

= 10\left( {{{|\overrightarrow {AB} {|^2} + |\overrightarrow {CA} {|^2} - |\overrightarrow {BC} {|^2}} \over {2.|\overrightarrow {CA} ||\overrightarrow {AB} {|}}}} \right)

= 10\left( {{{{{10}^2} + {7^2} - {8^2}} \over {2(10)(7)}}} \right)

= 10\left( {{{85} \over {140}}} \right)

= {{85} \over {14}}

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