If vectors A →$$=$$ $$cos$$ωt $$i^+$$$$sin$$ω$$tj^$$ and B→ $$=$$ $$cos$$ω$$t2i^+$$$$sin$$ω$$t2j^$$ are functions of time, then the value of t at which they are orthogonal to each other is:

Question

If vectors A →$$=$$ $$cos$$ωt $$i^+$$$$sin$$ω$$tj^$$  and  B→ $$=$$  $$cos$$ω$$t2i^+$$$$sin$$ω$$t2j^$$ are functions of time, then the value of t at which they are orthogonal to each other is:

Infinity Learn · Accepted Answer

A→ $$=$$ $$cos$$ω$$ti^+$$$$sin$$ωt $$j^B$$→ $$=$$ $$cos$$$$($$ω$$t2)i^+$$$$sin$$ω$$t2$$ $$j^For$$ A→  and  B→  orthogonal  A.→B→ $$=$$ $$0cos$$ωt $$i^+$$$$sin$$ωt $$j^$$.$$cos$$ω$$t2i^+$$$$sin$$ω$$t2j^$$ $$=$$ $$0cos$$ωt.$$cos$$ω$$t2+$$$$sin$$ωt.$$sin$$ω$$t2$$ $$=$$ $$0cos($$ω$$t-$$ω$$t2)$$ $$=0$$⇒ $$cos$$ω$$t2$$ $$=$$ $$0$$ω$$t2$$ $$=$$ π$$2$$ ⇒ ωt $$=$$ π  ⇒ t $$=$$ πω

If vectors $\vec{A} = cosωt \hat{i} + sinωt \hat{j} and \vec{B} = \cos \frac{ωt}{2} \hat{i} + \sin \frac{ωt}{2} \hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other is:

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If vectors A →= cosωt i^+sinωtj^ and B→ = cosωt2i^+sinωt2j^ are functions of time, then the value of t at which they are orthogonal to each other is:

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Ready to Test Your Skills?

free study material

If vectors $\vec{A} = cosωt \hat{i} + sinωt \hat{j} and \vec{B} = \cos \frac{ωt}{2} \hat{i} + \sin \frac{ωt}{2} \hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other is: