Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
673 views
in Algebra by (115k points)
closed by

A vector \(\vec r=a \hat i+b \hat j\) is equally inclined to both x and y axes. If the magnitude of the vector is 2 units, then what are the values of a and b respectively?


1. \(\dfrac{1}{2}, \dfrac{1}{2}\)
2. \(\dfrac{1}{\sqrt2}, \dfrac{1}{\sqrt2}\)
3. √2, √2
4. 2, 2

1 Answer

0 votes
by (114k points)
selected by
 
Best answer
Correct Answer - Option 3 : √2, √2

CONCEPT:

The scalar product of two vectors \(\vec a \ and \ \vec b \)is given by \(\vec a \cdot \;\vec b = \left| {\vec a} \right| \times \left| {\vec b} \right|\cos θ \)

CALCULATION:

Given: Vector \(\vec r=a \hat i+b \hat j\) is equally inclined to both x and y axes and the magnitude of the vector is 2 units.

i.e \(|\vec r| = 2\)

⇒ \(\sqrt {a^2 + b^2} = 2\)

⇒ a2 + b2 = 4 --------(1)

∵ The vector \(\vec r=a \hat i+b \hat j\) is equally inclined to both x and y axes

Let θ be the angle between the vector \(\vec r=a \hat i+b \hat j\) and both the x and y axes.

⇒ \(cos \ \theta = \frac{a}{2} = \frac{b}{2}\)

⇒ a = b

So, by substituting a = b in equation (1), we get

⇒ 2b2 = 4 ⇒ b = √2

So, a = b = √2

Hence, correct option is 3

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...