Which of the following statements are true? I. The zero vector has no definite direction. II. 2 i - 3 j + 4 k and -4 i + 6 j - 8 k are collinear. III. Two vectors with the same magnitude are equal. IV. A unit vector has magnitude 1.

Question 15

MediumOriginal question

Which of the following statements are true?
I. The zero vector has no definite direction.
II. $2\hat{i} - 3\hat{j} + 4\hat{k}$ and $-4\hat{i} + 6\hat{j} - 8\hat{k}$ are collinear.
III. Two vectors with the same magnitude are equal.
IV. A unit vector has magnitude 1.

All four: I, II, III and IVCorrect answerYour answerI and IV onlyCorrect answerYour answerI, II and IV onlyCorrect answerYour answerII, III and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I and IV are definitions. II: the second is $-2$ times the first, so they are collinear.
III is false: equal vectors need the same magnitude and the same direction.

Worth noting

Collinear vectors can point opposite ways; a negative multiple still lies on the same line.

Concept: Types of vectors
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsVectors and their types

Practise this chapter →

Ten questions from Vectors, at your own pace.

Explanation