Show that the line x=(2i^−2j^+3k^)+λ(i^−j^+4k^) is parallel to the plane r⋅(i^+5j^+k^)=7.

Given that the line x=(2i^−2j^+3k^)+λ(i^−j^+4k^) is parallel to the plane r⋅(i^+5j^+k^)=7.Direction ratios of the line are 1,−1,4.Direction ratios of normal to the plane are 1,5,1.∴(1×1)+(−1)×5+(4×1)=0.So, the given line is perpendicular to the normal of the given plane.Hence, the given line is parallel to the given plane.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Show that the line {x}=(2{i}-2{j}+3{k})+({i}-{j}+4{k}) is para

Question

Show that the line $x = (2 \hat{i} - 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + 4 \hat{k})$ is parallel to the plane $r \cdot (\hat{i} + 5 \hat{j} + \hat{k}) = 7$ .

Views: 815 students

Found 3 tutors discussing this question

Sofia Discussed

Show that the line

x = (2 \hat{i} - 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + 4 \hat{k})

is parallel to the plane

r \cdot (\hat{i} + 5 \hat{j} + \hat{k}) = 7

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Given that the line

x = (2 \hat{i} - 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + 4 \hat{k})

is parallel to the plane

r \cdot (\hat{i} + 5 \hat{j} + \hat{k}) = 7

Direction ratios of the line are

1, - 1, 4

Direction ratios of normal to the plane are

1, 5, 1

∴ (1 \times 1) + (- 1) \times 5 + (4 \times 1) = 0

So, the given line is perpendicular to the normal of the given plane.

Hence, the given line is parallel to the given plane.

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	Show that the line $x = (2 \hat{i} - 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + 4 \hat{k})$ is parallel to the plane $r \cdot (\hat{i} + 5 \hat{j} + \hat{k}) = 7$ .
Answer Type	Text solution:1
Upvotes	150

Show that the line x=(2i^−2j^​+3k^)+λ(i^−j^​+4k^) is parallel to the plane r⋅(i^+5j^​+k^)=7.

Text solutionVerified

Practice questions from similar books

Show that the line $x = (2 \hat{i} - 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + 4 \hat{k})$ is parallel to the plane $r \cdot (\hat{i} + 5 \hat{j} + \hat{k}) = 7$ .