Back to 3D PLANES

Your Progress

0 / 5 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • 3D PLANES

3d planes practice · Hard

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →

1 Hard

1 of 5

Understanding +4 | -1

The plane

a x+

=0

is rotated through an angle

\alpha

about its line of intersection with the plane

z=0

. If the equation of plane in new position is

\mathrm{ax}+\mathrm{by} \pm \mathrm{z} \sqrt{\mathrm{a}^2+\mathrm{b}^2} \tan \alpha+\mathrm{c}=0

. Find c.

View answer and explanation

Correct option: A

Option A (0) is correct because the equation of the rotated plane passes through the line of intersection of the original plane and z=0, resulting in c=0.

2 Hard

2 of 5

Application +4 | -1

(x,\,y,\,z)

be an arbitrary point lying on a plane

P

, which passes through the points

\mathrm{(42,}\,\mathrm{0,}\,\mathrm{0),}\,\,\mathrm{(0,}\,\mathrm{42,}\,\mathrm{0)}

and

\mathrm{(0,}\,\mathrm{0,}\,\mathrm{42)}

, then the value of expression

3 + \frac{{x - 11}}{{{{\left( {y - 19} \right)}^2}{{\left( {z - 12} \right)}^2}}} + \frac{{y\, - \,19}}{{{{\left( {x - 11} \right)}^2}{{\left( {z - 12} \right)}^2}}}\, + \frac{{z - 12}}{{{{\left( {x - 11} \right)}^2}{{\left( {y - 19} \right)}^2}}} - \frac{{x\mathrm{ } + \mathrm{ }y\mathrm{ } + z}}{{14\left( {x - 11} \right)\left( {y - 19} \right)\left( {z - 12} \right)}}

is equal to

View answer and explanation

Correct option: B

Option B (3) is correct because by substituting the plane equation into the expression and simplifying using the given condition, the expression reduces to 3.

3 Hard

3 of 5

Application +4 | -1

What is the length of the projection of

3 \hat{i}+4 \hat{j}+5 \hat{k}

on the xy-plane?

View answer and explanation

Correct option: A

Option A (5) is correct because the projection onto the xy-plane is the magnitude of the vector's x and y components, which is

\sqrt{3^2 + 4^2} = 5

4 Hard

4 of 5

Application +4 | -1

Through the point

\mathrm{P}(1,2,2)

a plane is drawn at right angles to OP meets the axes in A, B, C. Find

\lambda

, if the area of the triangle

\mathrm{ABC}

(240+\lambda) / 8

View answer and explanation

Correct option: A

Option A (3) is correct because finding the area of the triangle formed by the plane and the axes, and then comparing with the given expression yields lambda=3.

5 Hard

5 of 5

Analyzing +4 | -1

If the equation of the plane containing the line

x+2 y+3 z-4=0=2 x+y-z+5

and perpendicular to the plane

\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+k)+\mu(\hat{i}-2 \hat{j}+3 k)

a x+b y+c z=4

, then

(a-b+c)

is equal to

View answer and explanation

Correct option: B

Option D (3654) is correct because by setting up ratios of consecutive binomial coefficients and solving for n and r, the coefficient of the fourth term can be calculated as 3654.

Revision notes and key takeaways

Review 3D PLANES in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 5 single-correct-answer MCQs on 3D PLANES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

Continue Your Practice

📚 Switch Set (HARD)

Chapter Sets

ALL 241 MCQs EASY 177 MCQs HARD 5 MCQs MEDIUM 59 MCQs

0 /5

0✓ 0✗

0% Accuracy