EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Three-Dimensional Geometry · Question 97 of 120

What is ( a₂ - a₁) · ( b₁ × b₂)?

Question 97

MediumOriginal question

Two lines are L1:r⃗=(i^+2k^)+λ(i^+2j^−k^)L_1: \vec{r} = (\hat{i} + 2\hat{k}) + \lambda(\hat{i} + 2\hat{j} - \hat{k}) and L2:r⃗=(j^−k^)+μ(2i^+j^+k^)L_2: \vec{r} = (\hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + \hat{k}).

What is (a2⃗−a1⃗)⋅(b1⃗×b2⃗)(\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1} \times \vec{b_2})?

Options for question 97

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. a2⃗−a1⃗=−i^+j^−3k^\vec{a_2} - \vec{a_1} = -\hat{i} + \hat{j} - 3\hat{k}.

  2. (−1)(3)+(1)(−3)+(−3)(−3)=−3−3+9=3(-1)(3) + (1)(-3) + (-3)(-3) = -3 - 3 + 9 = 3.

Worth noting

15 adds the three products without their signs.

Concept
The shortest distance between skew lines
Typical time
120 s
Your time
—
The rule this testsSkew lines and the shortest distance
Practise this chapter →

Ten questions from Three-Dimensional Geometry, at your own pace.

Practise this chapter →

Ten questions from Three-Dimensional Geometry, at your own pace.

Practise this chapterAll 120 questions in Three-Dimensional GeometryRevise the notes for Three-Dimensional Geometry