MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 5

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12th CBSE

IMPORTANT

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Find the volume of the parallelepiped with its edges represented by the vectors $\hat{i} + \hat{j}, \hat{i} + 2 \hat{j}$ and $\hat{i} + \hat{j} + π \hat{k}$ .

[Write answer excluding the units]

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Important Questions on Scalar Triple Product

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 6

If

\vec{a}, \vec{b}

are non-collinear vectors, then find the value of

[\vec{a} \vec{b} \hat{i}] \hat{i} + [\vec{a} \vec{b} \hat{j}] \hat{j} + [\vec{a} \vec{b} \hat{k}] \hat{k}

.

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 7

If the vectors

(\sec^{2} A) \hat{i} + \hat{j} + \hat{k}, \hat{i} + (\sec^{2} B) \hat{j} + \hat{k}, \hat{i} + \hat{j} + (\sec^{2} C) \hat{k}

are coplanar, then find the value of

{cosec}^{2} A + {cosec}^{2} B + {cosec}^{2} C

.

HARD

12th CBSE

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MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 8

For any two vectors

\vec{a}

and

\vec{b}

of magnitudes

3

and

4

respectively, write the value of

[\begin{array}{l} \vec{a} & \vec{b} & \vec{a} \times \vec{b} \end{array}] + (\vec{a} \cdot \vec{b})^{2}

.

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12th CBSE

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MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 9

If

[3 \vec{a} + 7 \vec{b} \vec{c} \vec{d}] = λ [\vec{a} \vec{c} \vec{d}] + μ [\vec{b} \vec{c} \vec{d}]

then find the value of

λ + μ

.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 10

If

\vec{a}, \vec{b}, \vec{c}

are non-coplanar vectors, then find the value of

\frac{\vec{a} \cdot (\vec{b} \times \vec{c})}{(\vec{c} \times \vec{a}) \cdot \vec{b}} + \frac{\vec{b} \cdot (\vec{a} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})}

.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)>Q 11

Find

\vec{a} \cdot (\vec{b} \times \vec{c})

, if

\vec{a} = 2 \hat{i} + \hat{j} + 3 \hat{k}, \vec{b} = - \vec{i} + 2 \vec{j} + \vec{k} and \vec{c} = 3 \hat{i} + \hat{j} + 2 \hat{k}

.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 1

If

\vec{a}

lies in the plane of vectors

\vec{b}

and

\vec{c}

, then which of the following is correct?

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 7 - Scalar Triple Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 2

The value of

[\vec{a} - \vec{b} \vec{b} - \vec{c} \vec{c} - \vec{a}]

, where

| \vec{a} | = 1, | \vec{b} | = 5, | \vec{c} | = 3

, is