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Suppose   and . If  is unit vector, then the maximum value of scalar triple product  is -

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Rajasthan Gram Vikas Adhikari (VDO) 27 Dec 2021 Shift 1 Official Paper
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Concept:

Scalar Triple Product: 

If , 

 and,

Then their scalar triple product is defined as,

Calculation:

Given:

We have,

Now, 

If  is a unit vector so, 

When, θ = 0°

Maximum value = 

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More Scalar Triple Product Questions

Q1.Let \(\rm\vec{a},\vec{b},\vec{c}\) be three non zero vectors such that \(\rm \vec{c}\) is a unit vector perpendicular to both \(\rm \vec{a}\) and \(\rm \vec{b}\). If the angle between \(\rm\vec{a}\) and \(\rm\vec{b}\) be \(\frac{\pi}{6}\) then \(\begin{bmatrix} \vec{a} &\vec{b}& \vec{c}\end{bmatrix}^2 \) is:
Q2.If \(\rm\vec{a},\vec{b}\) and \(\rm\vec{c}\) are three non-coplanar vectors, then the value of \(\rm \frac{\vec{a}.(\vec{b}\times\vec{c})}{\vec{b}.(\vec{c}\times\vec{a})}+\rm \frac{\vec{b}.(\vec{c}\times\vec{a})}{\vec{c}.(\vec{a}\times\vec{b})}+\rm \frac{\vec{c}.(\vec{b}\times\vec{a})}{\vec{a}.(\vec{b}\times\vec{c})}\) is:
Q3.The vectors λî + ĵ + 2k̂, î + λĵ − k̂ and 2î − ĵ + λk̂ are coplanar if
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Q6.Find the value of 'a' such that the vectors 2î - ĵ + k̂, î + 2ĵ - 3k̂ and 3î + aĵ + 5k̂ are coplanar.
Q7.Find the scalar triple product of the vectors \(\vec a = 2\hat i + 3\hat j + 4\hat k\;,\;\vec b = 3\hat i + 4\hat j + 6\hat k\;and\;\vec c = 2\hat i + 4\hat j + \hat k\)
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Q9.Consider the following statements in respect of a vector \(\vec c=\vec a+\vec b\), where \(|\vec a|=|\vec b|\ne0\): 1. \(\vec c\) is perpendicular to \((\vec a-\vec b).\) 2. \(\vec c\) is perpendicular to \(\vec a \times \vec b.\) Which of the above statement is/are correct?

More Vector Algebra Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 
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Q4.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
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Q8.Let ABC be a triangle such that \(\overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\vec{b}, \overrightarrow{A B}=\vec{c},|\vec{a}|=6 \sqrt{2},|\vec{b}|=2 \sqrt{3}\) and \(\vec{b} \cdot \vec{c}=12\) Consider the statements : \(\text { (S1): }|(\vec{a} \times \vec{b})+(\vec{c} \times \vec{b})|-|\vec{c}|=6(2 \sqrt{2}-1)\) \(\text { (S2): } \angle A C B=\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then
Q9.Let a unit vector which makes an angle of 60° with 2î + 2ĵ - k̂ and an angle of 45° with î - k̂ be \(\vec{C}\). Then \(\vec{C}+ \left(-\frac{1}{2}\hat{i} + \frac{1}{3\sqrt{2}}\hat{j} - \frac{\sqrt{2}}{3}\hat{k}\right)\) is:
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