Let V→θ=cos⁡θ+sec⁡θa^+cos⁡θ-secθb^, where a^ and b^ are unit vectors and the angle between a^ and b^ is 60^o, then the minimum value of V→^4 is equal…

Question

Let V→θ=cos⁡θ+sec⁡θa^+cos⁡θ-secθb^, where a^ and b^ are unit vectors and the angle between a^ and b^ is 60^o, then the minimum value of V→^4 is equal to

MARKS Content Team · Accepted Answer

Correct answer: 12. V→^2=cos⁡θ+sec⁡θa^+cos⁡θ-sec⁡θb^^2 =cos⁡θ+sec⁡θ^2+cos⁡θ-sec⁡θ^2+(cos⁡θ-sec⁡θ)(cos⁡θ+sec⁡θ) =3cos^2⁡θ+sec^2⁡θ≥2√3 ⇒ least value of V→^2=2√3 ⇒ least value of V→^4=12

Let $\vec{V} (θ) = (\cos θ + \sec θ) \hat{a} + (\cos θ - s e c θ) \hat{b}$ , where $\hat{a}$ and $\hat{b}$ are unit vectors and the angle between $\hat{a}$ and $\hat{b}$ is $60^{o}$ , then the minimum value of ${|\vec{V}|}^{4}$ is equal to

Solution

More Vector Algebra Questions

Let V→θ=cos⁡θ+sec⁡θa^+cos⁡θ-secθb^, where a^ and b^ are unit vectors and the angle between a^ and b^ is 60o, then the minimum value of V→4 is equal to

Solution

More Vector Algebra Questions

Let $\vec{V} (θ) = (\cos θ + \sec θ) \hat{a} + (\cos θ - s e c θ) \hat{b}$ , where $\hat{a}$ and $\hat{b}$ are unit vectors and the angle between $\hat{a}$ and $\hat{b}$ is $60^{o}$ , then the minimum value of ${|\vec{V}|}^{4}$ is equal to