If the vectors $$3a$$→−$$5b$$→ and $$2a$$→$$+b$$→ are mutually perpendicular and if a→$$+4b$$→ and b→−a→ are also mutually perpendicular, then the cosine of the angle between a→ and b→ is

Question

If the vectors  $$3a$$→−$$5b$$→ and $$2a$$→$$+b$$→ are mutually perpendicular and  if  a→$$+4b$$→ and b→−a→ are also mutually perpendicular, then the cosine of the angle between a→ and b→ is

Infinity Learn · Accepted Answer

(3a$$→−$$5b$$→$$)⋅(2a$$→$$+b$$→$$)=0$$ or  $$6$$|a→|$$2$$−$$5$$|b→|$$2=7a$$→⋅b→ Also, $$(a$$→$$+4b$$→$$)⋅$$(b$$→−a→$$)=0or$$  −|a→|$$2+4$$|b→|$$2=3a$$→⋅b→or  $$67$$|a→|$$2$$−$$57$$|b→|$$2=$$−$$13$$|a→|$$2+43$$|b→|$$2or$$ $$25$$|a→|$$2=43$$|b→|$$2$$⇒$$3a$$→⋅b→$$=$$−|a→|$$2+4$$|b→|$$2=5725$$|b→|$$2or$$  $$3$$|a→||b→|$$cos$$⁡θ$$=5725$$|b→|$$2or$$  $$34325$$|b→|$$2cos$$⁡θ$$=5725$$|b→|$$2or$$  $$cos$$⁡θ$$=19543$$

If the vectors $3 \vec{a} - 5 \vec{b} and 2 \vec{a} + \vec{b}$ are mutually perpendicular and if $\vec{a} + 4 \vec{b} and \vec{b} - \vec{a}$ are also mutually perpendicular, then the cosine of the angle between $\vec{a} and \vec{b}$ is

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If the vectors 3a→−5b→ and 2a→+b→ are mutually perpendicular and if a→+4b→ and b→−a→ are also mutually perpendicular, then the cosine of the angle between a→ and b→ is

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If the vectors $3 \vec{a} - 5 \vec{b} and 2 \vec{a} + \vec{b}$ are mutually perpendicular and if $\vec{a} + 4 \vec{b} and \vec{b} - \vec{a}$ are also mutually perpendicular, then the cosine of the angle between $\vec{a} and \vec{b}$ is