# NCERT Solutions For Class 12 Maths Chapter 4 Determinants Ex 4.3

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 4 |

Exercise | Class 12 Maths Chapter 4 Determinants Exercise 4.3 |

Number of Questions Solved | 5 |

## NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

**NCERT TEXTBOOK EXERCISES**

**Ex 4.3 Class 12 Maths Question 1.****Find the area of the triangle with vertices at the point given in each of the following:****(i) (1,0), (6,0) (4,3)****(ii) (2,7), (1,1), (10,8)****(iii) (-2,-3), (3,2), (-1,-8)**

**Solution:**

(i) Area of triangle = $\frac { 1 }{ 2 } \left| \begin{matrix} 1\quad & 0 & \quad 1 \ 6\quad & 0 & \quad 1 \ 4\quad & 3 & \quad 1 \end{matrix} \right|$

= 12 [1(0-3)+1(18-0)]

= 7.5 sq units

**Ex 4.3 Class 12 Maths Question 2.****Show that the points A (a, b + c), B (b, c + a) C (c, a+b) are collinear.**

**Solution:**

The vertices of âˆ†ABC are A (a, b + c), B (b, c + a) and C (c, a + b)

**Ex 4.3 Class 12 Maths Question 3.****Find the value of k if area of triangle is 4 square units and vertices are****(i) (k, 0), (4,0), (0,2)****(ii) (-2,0), (0,4), (0, k).**

**Solution:**

(i) Area of âˆ† = 4 (Given)

$\frac { 1 }{ 2 } \left| \begin{matrix} k\quad & 0 & \quad 1 \ 4\quad & 0 & \quad 1 \ 0\quad & 2 & \quad 1 \end{matrix} \right|$

= 12 [-2k+8]

= -k+4

Case (a): -k + 4 = 4 ==> k = 0

Case(b): -k + 4 = -4 ==> k = 8

Hence, k = 0,8

(ii) The area of the triangle whose vertices are (-2,0), (0,4), (0, k)

**Ex 4.3 Class 12 Maths Question 4.****(i) Find the equation of line joining (1, 2) and (3,6) using determinants.****(ii) Find the equation of line joining (3,1), (9,3) using determinants.**

**Solution:**

(i) Given: Points (1,2), (3,6)

Equation of the line is

**Ex 4.3 Class 12 Maths Question 5.****If area of triangle is 35 sq. units with vertices (2, â€“ 6), (5,4) and (k, 4). Then k is****(a) 12****(b) â€“ 2****(c) -12,-2****(d) 12,-2**

**Solution:**

(d) Area of âˆ† = $\frac { 1 }{ 2 } \left| \begin{matrix} 2\quad & -6 & \quad 1 \ 5\quad & 4 & \quad 1 \ k\quad & 4 & \quad 1 \end{matrix} \right|$

= 12 [50 â€“ 10k] = 25 â€“ 5k

âˆ´ 25-5k = 35 or 25-5k = -35

-5k = 10 or 5k = 60

=> k = -2 or k = 12

## NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3 PDF

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