In the isosceles triangle ABC,$$_$$|AB→|$$=$$|BC→|$$=8$$, a point E divides AB internally in the ratio $$1$$:$$3$$, then the cosine of the angle between CE→ and CA→ is : (where$$ |CA→|$$=12$$ $$)

Question

In the isosceles triangle ABC,$$_$$|AB→|$$=$$|BC→|$$=8$$, a point E divides AB internally in  the ratio $$1$$:$$3$$, then the cosine of the angle between CE→ and CA→ is : (where$$ |CA→|$$=12$$ $$)

Infinity Learn · Accepted Answer

Given |b→|$$=$$|b→−c→|$$=8$$ and |c→|$$=12$$|b→|$$2=$$|b→−c→|$$2$$ |b→|$$2=b$$→$$2+c$$→$$2-2b$$→·c→ b→·c→$$=1442=72c$$→$$-b$$→$$42=c$$→$$2-2c$$→·b→$$4+b$$→$$216$$ $$=144-724+6416=112$$ c→$$-b$$→$$4=112CE$$→$$=OE$$→$$-OC$$→$$=b$$→$$4-c$$→ CA→$$=-c$$→$$cos$$θ  $$=$$  c→ c→ −b→$$4$$|c→ | c→ − b→$$4$$     $$=$$  $$c2$$→ −  c→ ⋅ b→$$412c$$→ − b→$$4=144-1812112=12612$$×$$47=378$$

$In the isosceles triangle \underline{ABC,} | \vec{A B} | = | \vec{B C} | = 8, a point E divides AB internally in$ $the ratio 1 : 3, then the cosine of the angle between \vec{C E} and \vec{C A} is : (where | \vec{C A} | = 12)$

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In the isosceles triangle ABC,_|AB→|=|BC→|=8, a point E divides AB internally in the ratio 1:3, then the cosine of the angle between CE→ and CA→ is : (where |CA→|=12 )

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$In the isosceles triangle \underline{ABC,} | \vec{A B} | = | \vec{B C} | = 8, a point E divides AB internally in$ $the ratio 1 : 3, then the cosine of the angle between \vec{C E} and \vec{C A} is : (where | \vec{C A} | = 12)$