Sample QuestionsScalar Triple Product questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\vec{\text{a}} $ lies in the plane of vectors $\vec{\text{b}}$ and $\vec{\text{c}},$ then which of the following is correct?
- $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]=0$
- $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]=1$
- $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]=3$
- $\big[\vec{\text{b}}\vec{\text{c}}\vec{\text{a}}\big]=1$
View full solution →If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+5\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}-4\hat{\text{j}}+5\hat{\text{k}}$ and $\vec{\text{c}}=5\hat{\text{i}}-3\hat{\text{j}}-2\hat{\text{k}},$ then the volume of the parallelopiped with contermious edges $\vec{\text{a}}+\vec{\text{b}},\vec{\text{b}}+\vec{\text{c}},\vec{\text{c}}+\vec{\text{a}}$ is:
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2
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1
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-1
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0
View full solution →If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three non-coplanar vectors, then $\big(\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big).\big[\big(\vec{\text{a}}+\vec{\text{b}}\big)\times\big(\vec{\text{a}}+\vec{\text{c}}\big)\big]$ equals:
- $0$
- $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
- $2\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
- $-\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
View full solution →$\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big\{\big(\vec{\text{a}}-\vec{\text{b}}\big)\times\big(\vec{\text{a}}-\vec{\text{b}}-\vec{\text{c}}\big)\big\}$ is equal to:
- $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
- $2\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
- $3\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
- $0$
View full solution →If $\big[2\vec{\text{a}}+4\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big]=\lambda\big[\vec{\text{a}}\vec{\text{c}}\vec{\text{d}}\big]+\mu\big[\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big],$ then $\lambda+\mu=$
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6
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-6
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10
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8
View full solution →Write the value of $\big[\hat{\text{i}}-\hat{\text{j }}\hat{\text{j}}-\hat{\text{k }}\hat{\text{k}}-\hat{\text{i}}\big].$
View full solution →If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-coplanar vectors, then find the value of $\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$
View full solution →Find the volume of the parallelopiped with its edges represented by the vectors
$\hat{\text{i}}+\hat{\text{j}},\hat{\text{i}}+2\hat{\text{j}}$ and $\hat{\text{i}}+\hat{\text{j}}+\pi{\text{k}}.$
View full solution →Write the value of $\big[2\hat{\text{i }} 3\hat{\text{j }}4\hat{\text{k}}\big].$
View full solution →Show that the following triads of vectors are coplanar:
$\vec{\text{a}}=-4\hat{\text{i}}-6\hat{\text{j}}-2\hat{\text{k}},\vec{\text{b}}=-\hat{\text{i}}+4\hat{\text{j}}+3\hat{\text{k}},\vec{\text{c}}=-8\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$
View full solution →For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ of magnitudes 3 and 4 respectively, write the value of $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{a}}\times\vec{\text{b}}\big]+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$
View full solution →Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
$\vec{\text{a}}=11\hat{\text{i}},\vec{\text{b}}=2\hat{\text{j}},\vec{\text{c}}=13\hat{\text{k}}$
View full solution →Let $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}$ and $\vec{\text{c}}=\text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}}.$ Then,
If $c_{1 }= 1$ and $c_{2 }= 2,$ find $c_3$ which makes $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ coplanar.
View full solution →Find the volume of the parallelopiped whose coterminous edges are represented by the vectore:
$\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$
View full solution →Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
$\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}},\vec{\text{c}}=3\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$
View full solution →If the vectors $\big(\sec^2\text{A}\big)\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\hat{\text{i}}+\big(\sec^2\text{B}\big)+\hat{\text{k}},\hat{\text{i}}+\hat{\text{j}}+\big(\sec^2\text{C}\big)\hat{\text{k}}$ are coplanar, then find the value of $\text{cosec}^2\text{A}+\text{cosec}^2\text{B}+\text{cosec}^2\text{C}.$
View full solution →Find $\lambda$ for which the points A(3, 2, 1), B(4, $\lambda$, 5), C(4, 2, -2) and D(6, 5, -1) are coplanar.
View full solution →Find the value of $\lambda$ for which the four points with position vectors
$-\hat{\text{j}}-\hat{\text{k}},4\hat{\text{i}}+5\hat{\text{j}}+\lambda\hat{\text{k}},3\hat{\text{i}}+9\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+4\hat{\text{j}}+4\hat{\text{k}}$ are co planar.
View full solution →Show that four points whose position vectors are
$6\hat{\text{i}}-7\hat{\text{j}},16\hat{\text{i}}-19\hat{\text{j}}-4\hat{\text{k}},3\hat{\text{i}}-6\hat{\text{k}},2\hat{\text{i}}-5\hat{\text{j}}+10\hat{\text{k}}$ are coplanar.
View full solution →$\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are the position vectors of points A, B and C respectively, prove that:
$\vec{\text{a}}\times\vec{\text{b}}+\vec{\text{b}}\times\vec{\text{c}}+\vec{\text{c}}\times\vec{\text{a}}$ is a vector perpendicular to the plane of triangle ABC.
View full solution →