Start learning →

GRE Unit 8A: Areas Between Curves — practice questions — page 2

Explore 37 free Unit 8A: Areas Between Curves questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Unit 8A: Areas Between Curves with Quill →

Unit 8A: Areas Between Curves questions and exercises with answers

Showing questions 31–37 of 37.

The direction cosines of a line whose direction ratios are $2,-1,2$ are:Read the answer and worked solution →The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:Read the answer and worked solution →The cartesian equation of a line through $(x_1,y_1,z_1)$ with direction ratios $a,b,c$ is:Read the answer and worked solution →A line makes equal angles with the three coordinate axes. Its direction cosines are:Read the answer and worked solution →A line with direction ratios $(k,2,3)$ is perpendicular to a line with direction ratios $(1,-2,1)$. Then $k$ equals:Read the answer and worked solution →The distance of the point $(2,3,4)$ from the origin is:Read the answer and worked solution →If a line makes angles $90^\circ, 60^\circ, 30^\circ$ with the x, y, z axes, the sum of squares of its direction cosines is:Read the answer and worked solution →

Worked practice questions

The direction cosines of a line whose direction ratios are $2,-1,2$ are:

  1. $2, -1, 2$
  2. $\tfrac12, -\tfrac11, \tfrac12$
  3. $\tfrac29, -\tfrac19, \tfrac29$
  4. $\tfrac23, -\tfrac13, \tfrac23$
Show answer and solution

Correct answer: D. $\tfrac23, -\tfrac13, \tfrac23$

Divide by √(2²+1²+2²)=3: direction cosines are (2/3, −1/3, 2/3).

Open this question →

The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:

  1. $\tfrac{4}{9}$
  2. $\tfrac{2}{3}$
  3. $\tfrac{1}{9}$
  4. $\tfrac{8}{9}$
Show answer and solution

Correct answer: D. $\tfrac{8}{9}$

We have cosθ = (1·2+2·2+2·1)/(√9·√9). So cosθ = 8/9.

Open this question →

The cartesian equation of a line through $(x_1,y_1,z_1)$ with direction ratios $a,b,c$ is:

  1. $\tfrac{x-x_1}{a}+\tfrac{y-y_1}{b}+\tfrac{z-z_1}{c}=1$
  2. $\tfrac{a}{x-x_1}=\tfrac{b}{y-y_1}=\tfrac{c}{z-z_1}$
  3. $\tfrac{x-x_1}{a}=\tfrac{y-y_1}{b}=\tfrac{z-z_1}{c}$
  4. $ax+by+cz=0$
Show answer and solution

Correct answer: C. $\tfrac{x-x_1}{a}=\tfrac{y-y_1}{b}=\tfrac{z-z_1}{c}$

The symmetric (cartesian) form of a line is (x−x₁)/a = (y−y₁)/b = (z−z₁)/c.

Open this question →

How to practise

  1. Choose a Unit 8A: Areas Between Curves question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Unit 8A: Areas Between Curves practice for GRE. Read explanations as you go. No signup form needed to start.

Practise Unit 8A: Areas Between Curves →

More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann Sums