NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise Solutions

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise is provided in this article with a step by step explanation. Chapter 10 Vector Algebra Miscellaneous Exercise Solutions covers basic concepts of types of vectors, the addition of vectors, and the product of two vectors.

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Class 12 Chapter 10 Vector Algebra Topics:

Position vector	Direction cosines	Unit vector
Negative of a vector	Triangle law of vector addition	Properties of vector addition
Properties of scalar product of two vectors	Laws of Vector Addition	Vector Formula
Magnitude of a vector	Vector Projection Formula	Scalar triple product of vectors
Cross product	Vector Calculus	Vector Space

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Math Formula	Arithmetic
Trigonometry	Math Study Notes	Calculus
Difference between in Maths	Mensuration	Math MCQs

CBSE CLASS XII Related Questions

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

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2.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

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3.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

\( \frac{7\pi}{12} \)
\( \frac{5\pi}{12} \)
\( -\frac{5\pi}{12} \)
\( \frac{\pi}{3} \)

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4.
If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that
\[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]

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5.
If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

\(0.35\)
\(0.85\)
\(0.5\)
\(0.21\)

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6.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise

CBSE CLASS XII Related Questions

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

3.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

4.
If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that
\[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]

5.
If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

6.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise

CBSE CLASS XII Related Questions

1.Find the value of \(x\) if \(A = B\), where\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.Evaluate :\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

3.The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

4.If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that\[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]

5.If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

6.Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

3.
The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

4.
If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that
\[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]

5.
If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

6.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).