JEE MAIN - Mathematics (2021 - 18th March Evening Shift - No. 10)
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 :
$${{25} \over 4}$$
$${{127} \over 20}$$
$${{85} \over 14}$$
$${{115} \over 16}$$
Explanation
_18th_March_Evening_Shift_en_10_2.png)
$$|\overrightarrow a | = 8,|\overrightarrow b | = 7,|\overrightarrow c | = 10$$
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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