RD Sharma Solution for Class 12 Chapter 24- Download PDF
- RD Sharma Solution for Class 12 Chapter 24 - Question with Answers
FAQs on Scalar or Dot Product

RD Sharma Solutions for Class 12 Maths Chapter 24 – Scalar or Dot Product

Q: What is the general form of a straight line?

The general form is Ax + By + C = 0 , where A, B, and C are constants, and A and B are not both zero.

Q: What does the slope of a line represent?

The slope represents the inclination or steepness of the line. It tells us how much the line rises or falls for each unit of horizontal change.

Q: What is the normal form of a line?

The normal form is: x cos ⁡ α + y sin ⁡ α = p x \cos \alpha + y \sin \alpha = p x cos α + y sin α = p where α \alpha α is the angle the perpendicular makes with the x-axis and p p p is the length of the perpendicular from the origin.

By Swati Singh

Updated on 6 May 2025, 11:20 IST

RD Sharma Class 12 Solutions for Chapter 12 on Scalar (Dot) Product are designed to help students strengthen their understanding of vector algebra. These step-by-step solutions serve as a reliable guide while solving exercises from the RD Sharma textbook, making practice more effective and organized. To support flexible learning, all solutions are also available in PDF format, so students can access them anytime based on their convenience.

When working through RD Sharma’s Class 12 textbook, having a dependable reference like these solutions is highly beneficial. They help in clearing doubts quickly and provide the right approach to tackle each problem as per the latest CBSE syllabus and marking guidelines.

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In vector algebra, a vector is defined by both direction and magnitude. When two vectors are multiplied using a scalar or dot product, the result is a real number. The dot product, denoted with a central dot (·), is an algebraic operation that involves multiplying two sequences of numbers of the same length to produce a scalar.

This concept can be interpreted both algebraically and geometrically. From a geometric perspective, it relates to the angle between vectors and their magnitudes.

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To gain a deeper understanding and improve your problem-solving skills, explore the RD Sharma Solutions for Class 12. These solutions simplify complex topics and are an excellent resource for exam preparation.

RD Sharma Solution for Class 12 Chapter 24- Download PDF

Here are the RD Sharma Solutions Class 12 Maths Chapter 24 Scalar or Dot Product Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores

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RD Sharma Solution for Class 12 Chapter 24 - Question with Answers

What is the general form of a line?
It is written as A x plus B y plus C equals zero.

How do you calculate the slope between two points?
Subtract the y-values and divide by the difference of x-values.

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What does slope represent?
Slope shows how steep the line is.

When are two lines parallel?
Two lines are parallel when their slopes are equal.

When are two lines perpendicular?
When the product of their slopes is negative one.

How do you find the x-intercept?
Set y equal to zero and solve for x.

How do you find the y-intercept?
Set x equal to zero and solve for y.

What is slope-intercept form?
It is y equals m x plus c, where m is slope and c is y-intercept.

What is intercept form of a line?
It is x over a plus y over b equals one.

What is point-slope form?
It uses a point and the slope to write the equation.

What does an undefined slope mean?
The line is vertical.

What does zero slope mean?
The line is horizontal.

How can you check if a point lies on a line?
Substitute the point into the equation. If both sides match, it lies on the line.

What is the normal form of a line?
It involves cosine and sine of the angle with the x-axis.

What is the distance from a point to a line?
Use the formula involving the coefficients of the line and the point.

What does a vertical line look like?
It is written as x equals a constant.

What does a horizontal line look like?
It is written as y equals a constant.

Can three points lie on one straight line?
Only if they are collinear.

How do you find if three lines meet at one point?
Solve two equations and check if the third also satisfies the result.

How do you find where two lines intersect?
Solve their equations together.

What is the angle between two lines?
It depends on the difference in their slopes.

What does it mean if two lines are the same?
All their coefficients are in the same ratio.

How do you find a line parallel to another through a given point?
Use the same slope and pass it through the given point.

How do you find a line perpendicular to another through a given point?
Use the negative reciprocal of the given slope and apply point-slope form.

What is a line segment?
A line with two fixed endpoints.

What is a ray?
A line that starts at one point and extends in one direction endlessly.

What is the shortest distance from a point to a line?
It is the perpendicular distance.

How do you know if two lines are neither parallel nor perpendicular?
If their slopes are different and not negative reciprocals.

How do you convert slope-intercept form to general form?
Bring all terms to one side of the equation.

What is meant by collinear points?
Points that lie on the same straight line.

What is meant by concurrent lines?
Lines that meet at a single point.

Can a line intersect a circle more than twice?
No, at most it can intersect at two points.

What is the locus of a point equidistant from two lines?
It is the angle bisector of the region between the lines.

How do you find the foot of perpendicular from a point to a line?
Use coordinate geometry methods or formulas involving slopes.

What happens to a line if its slope increases?
The line becomes steeper.

FAQs on Scalar or Dot Product

What is the general form of a straight line?

The general form is Ax + By + C = 0, where A, B, and C are constants, and A and B are not both zero.

How do you find the slope of a line passing through two points?

Use the formula:

\text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}

$Slope (m)$ $=$ $x$ $2$ $$ $-$ $x$ $1$ $$ $y$ $2$ $$ $-$ $y$ $1$ $$ $$

What does the slope of a line represent?

The slope represents the inclination or steepness of the line. It tells us how much the line rises or falls for each unit of horizontal change.

How can we find if two lines are parallel or perpendicular?

Parallel lines: Their slopes are equal: $m_1 = m_2$ $m$ $1$ $$ $=$ $m$ $2$ $$
Perpendicular lines: Product of slopes = -1: $m_1 \cdot m_2 = -1$ $m$ $1$ $$ $\cdot$ $m$ $2$ $$ $=$ $-1$

What is the condition for three lines to be concurrent?

Three lines are concurrent if they intersect at a single point. Solve any two equations to find the point, and check if it satisfies the third.

What is the normal form of a line?

The normal form is:

x \cos \alpha + y \sin \alpha = p

$x$ $cos$ $α$ $+$ $y$ $sin$ $α$ $=$ $p$

where $\alpha$ $α$ is the angle the perpendicular makes with the x-axis and $p$ $p$ is the length of the perpendicular from the origin.

What types of questions are asked from this chapter in board exams?

Questions based on:

Finding slope and intercepts
Deriving equations of lines
Angle between lines
Distance from a point to a line
Condition of concurrency or perpendicularity
are commonly asked.

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RD Sharma Solution for Class 12 Chapter 24- Download PDF
- RD Sharma Solution for Class 12 Chapter 24 - Question with Answers
FAQs on Scalar or Dot Product

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