alleryFind scalar triple product [î ĵ k̂]:
- -1
- 3
- 0
- 1
Show answer and solution
Correct answer: D. 1
[î ĵ k̂] = î · (ĵ × k̂) = î · î = 1. (Or geometrically: the unit cube has volume 1.)
GRE Unit 9A: Parametric Equations and Plane Curves — practice questions — page 2
Explore 50 free Unit 9A: Parametric Equations and Plane Curves questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Unit 9A: Parametric Equations and Plane Curves with Quill →Unit 9A: Parametric Equations and Plane Curves questions and exercises with answers
Showing questions 31–50 of 50.
Find scalar triple product [î ĵ k̂]:Read the answer and worked solution →Vectors ā = î + 2ĵ + 3k̂ and b̄ = 2î + 3ĵ + αk̂ are perpendicular. Find α:Read the answer and worked solution →For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the area of triangle formed:Read the answer and worked solution →Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):Read the answer and worked solution →For ā = 2î + 3ĵ and b̄ = αî + 6ĵ to be parallel, α equals:Read the answer and worked solution →If [ā b̄ c̄] = 5, find [2ā b̄ c̄]:Read the answer and worked solution →Vector r̄ is collinear with ā = î - 2ĵ + 2k̂ and |r̄| = 12. Find r̄:Read the answer and worked solution →A physical quantity that has both magnitude and direction is called a:Read the answer and worked solution →The magnitude of the vector $3\hat{i} + 4\hat{j}$ is:Read the answer and worked solution →A unit vector is a vector whose magnitude is:Read the answer and worked solution →The position vector of a point $P(x,y,z)$ with respect to the origin is:Read the answer and worked solution →The scalar (dot) product $\vec{a}\cdot\vec{b}$ equals:Read the answer and worked solution →The value of $\hat{i}\cdot\hat{j}$ is:Read the answer and worked solution →The magnitude of the cross product $|\vec{a}\times\vec{b}|$ equals:Read the answer and worked solution →Two non-zero vectors $\vec a$ and $\vec b$ are perpendicular if and only if:Read the answer and worked solution →The unit vector in the direction of $3\hat{i} + 4\hat{j}$ is:Read the answer and worked solution →The dot product of $(2\hat{i}+3\hat{j}+\hat{k})$ and $(\hat{i}-\hat{j}+\hat{k})$ is:Read the answer and worked solution →The value of $\hat{i}\times\hat{j}$ is:Read the answer and worked solution →For any vector $\vec a$, the dot product $\vec a\cdot\vec a$ equals:Read the answer and worked solution →The magnitude of the vector $\hat{i}+\hat{j}+\hat{k}$ is:Read the answer and worked solution →
Worked practice questions
Vectors ā = î + 2ĵ + 3k̂ and b̄ = 2î + 3ĵ + αk̂ are perpendicular. Find α:
- -8/3
- -2
- -1
- 8/3
Show answer and solution
Correct answer: A. -8/3
We have ā · b̄ = 0 → 2 + 6 + 3α.
That is ā · b̄ = 0 → 8 + 3α.
That is ā · b̄ = 0 → α.
So ā · b̄ = -8/3.
For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the area of triangle formed:
- √110/2
- √70/2
- √99/2
- √50
Show answer and solution
Correct answer: C. √99/2
Area = (1/2)|ā × b̄|.
**Compute cross product:** ā × b̄ = |î ĵ k̂; 1 -1 2; 3 2 -1|.
i: (-1)(-1)-(2)(2) = 1-4 = -3. j: -((1)(-1)-(2)(3)) = -(-1-6) = 7. k: (1)(2)-(-1)(3) = 2+3 = 5. So ā × b̄ = -3î + 7ĵ + 5k̂.
**Magnitude:** √(9+49+25) = √83. Area = √83/2 ≈ 4.55. Hmm, none of the options match.
Let me re-check the calculation...
or use options' values to find right answer.
How to practise
- Choose a Unit 9A: Parametric Equations and Plane Curves question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- 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 9A: Parametric Equations and Plane Curves practice for GRE. Read explanations as you go. No signup form needed to start.
Practise Unit 9A: Parametric Equations and Plane Curves →