Vector Basics

From definition of dot product of vectors, we have

x%5C%2C.%5C%2Cy%3Dxy%5C%2C%5C%2C%5Ccos%20%5C%2C%5C%2C%5Ctheta

When

%5Ctheta%20%3D%7B%7B90%7D%5E%7Bo%7D%7D%2C%5C%2C%5C%2C%5C%2C%5Ccos%20%5C%2C%5C%2C%7B%7B90%7D%5E%7Bo%7D%7D%3D0

%5Ctherefore

x%5C%2C.%5C%2Cy%3D0

Given,

x%3Da%5C%2C%5Ccos%20%5C%2C%5Ctheta%20%5C%2C%5Chat%7Bi%7D%2Bb%5C%2C%5Csin%20%5C%2C%5Ctheta%20%5C%2C%5Chat%7Bj%7D

y%3Db%5C%2Csin%5C%2C%5C%2C%5Ctheta%20%5C%2C%5C%2C%5Chat%7Bi%7D-a%5C%2C%5Ccos%20%5C%2C%5C%2C%5Ctheta%20%5C%2C%5Chat%7Bj%7D

x%5C%2C.%5C%2Cy%3D(a%5C%2C%5Ccos%20%5C%2C%5C%2C%5Ctheta%20%5C%2C%5C%2C%5Chat%7Bi%7D%2Bb%5C%2Csin%5C%2C%5C%2C%5Ctheta%20%5C%2C%5Chat%7Bj%7D)

(b%5C%2Csin%5C%2C%5C%2C%5Ctheta%20%5C%2C%5C%2C%5Chat%7Bi%7D-a%5C%2C%5Ccos%20%5C%2C%5C%2C%5Ctheta%20%5C%2C%5Chat%7Bj%7D)

x%5C%2C.%5C%2Cy%3Dab%5C%2C%5C%2C%5Csin%20%5C%2C%5Ctheta%20%5C%2C%5C%2C%5Ccos%20%5C%2C%5Ctheta%20%5C%2C-%5C%2Cab%5C%2C%5C%2C%5C%2C%5Csin%20%5C%2C%5Ctheta%20%5C%2C%5C%2C%5Ccos%20%5C%2C%5Ctheta%20%5C%2C%3D0

Hence, vectors are perpendicular.
Similarly for option and also

x.y%3D0

About Vector Basics - KCET

Vector Basics is a vital chapter for KCET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Vector Basics PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Vector Basics carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

About Vector Basics - KCET

Frequently Asked Questions

Why focus on Vector Basics PYQs?

How to best use this analysis?

Vector Basics

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

About Vector Basics - KCET

Frequently Asked Questions

Why focus on Vector Basics PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs