NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1 is covered in this article with a detailed explanation. Chapter 10 Vector Algebra Exercise 10.1 covers basic concepts of the position vector, types of vectors, and direction cosines.

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Class 12 Chapter 10 Vector Algebra Topics:

Addition of vectors	Properties of vector addition	Laws of Vector Addition
Negative of a vector	Vector Projection Formula	Vector Formula
Triangle law of vector addition	Direction of a vector	Components of vector
Vector Space	Vector Calculus	Multiplication of vector with scalar

CBSE Class 12 Mathematics Study Guides:

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

CBSE CLASS XII Related Questions

1.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

\(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
\(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
\(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
\(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

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2.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

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3.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

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4.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

5.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

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6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1

CBSE CLASS XII Related Questions

1.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

2.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

3.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

4.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

5.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1

CBSE CLASS XII Related Questions

1.Find:Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

2.If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

3.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

4.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

5. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

6.Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

2.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

3.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

4.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

5.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]