Assertion (A): The vector $3\hat{i} - 2\hat{j} + 6\hat{k}$ makes an obtuse angle with the $y$ -axis.
Reason (R): The cosine of the angle a vector makes with the $y$ -axis is its $\hat{j}$ component divided by its magnitude.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

R is true: it is the direction cosine $m = \frac{a_2}{\lvert \vec{a} \rvert}$ .
Here $m = -\frac{2}{7} < 0$ , so the angle is obtuse: A is true, and R is the reason.

Concept: The angle a vector makes with an axis
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsVectors and their types

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Ten questions from Vectors, at your own pace.

Assertion (A): The vector 3i^−2j^+6k^3\hat{i} - 2\hat{j} + 6\hat{k}3i^−2j^​+6k^ makes an obtuse angle with the yyy-axis.Reason (R): The cosine of the angle a vector makes with the yyy-axis is its j^\hat{j}j^​ component divided by its magnitude.

Explanation

Assertion (A): The vector $3\hat{i} - 2\hat{j} + 6\hat{k}$ makes an obtuse angle with the $y$ -axis.
Reason (R): The cosine of the angle a vector makes with the $y$ -axis is its $\hat{j}$ component divided by its magnitude.