Find the angle between the planes r⋅(i^+j^)=1 and r⋅(i^+k^)=3.

Given planes are x+1=1 and x+z=3The direction ratio of normals to these planes are 1,1,0 and 1,0,1∴cosθ={12+12+02}{12+02+12}∣(1×1)+(1×0)+(0×1)∣=(2×2)1=21The angle between the planes is⇒θ=3π.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Find the angle between the planes {r} ({i}+{j})=1 and {r} ({i}

Question

Find the angle between the planes $r \cdot (\hat{i} + \hat{j}) = 1$ and $r \cdot (\hat{i} + \hat{k}) = 3$ .

Views: 714 students

Found 3 tutors discussing this question

Mateo Discussed

Find the angle between the planes

r \cdot (\hat{i} + \hat{j}) = 1

and

r \cdot (\hat{i} + \hat{k}) = 3

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Given planes are

x + 1 = 1

and

x + z = 3

The direction ratio of normals to these planes are

1, 1, 0

and

1, 0, 1

∴ cos θ = \frac{∣ ( 1 \times 1 ) + ( 1 \times 0 ) + ( 0 \times 1 ) ∣}{{ 1 ^{2} + 1 ^{2} + 0 ^{2} } { 1 ^{2} + 0 ^{2} + 1 ^{2} }}

= \frac{1}{( 2 \times 2 )} = \frac{1}{2}

The angle between the planes is

\Rightarrow θ = \frac{π}{3}

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Find the angle between the planes $r \cdot (\hat{i} + \hat{j}) = 1$ and $r \cdot (\hat{i} + \hat{k}) = 3$ .
Answer Type	Text solution:1
Upvotes	150

Find the angle between the planes r⋅(i^+j^​)=1 and r⋅(i^+k^)=3.

Text solutionVerified

Practice questions from similar books

Find the angle between the planes $r \cdot (\hat{i} + \hat{j}) = 1$ and $r \cdot (\hat{i} + \hat{k}) = 3$ .