Direction of λ\(\vec{a}\) and \(\vec{a}\) is same if λ is _______

(a) imaginary

(b) negative

(c) positive

(d) zero

This question was addressed to me during an online interview.

This intriguing question originated from Multiplication of a Vector by a Scalar topic in chapter Vector Algebra of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

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The correct option is (c) positive

To explain: Direction of λ\vec{a} and \vec{a} is same if value λ is positive as it gives it a direction which is positive in nature. If the value of λ is negative then the direction of the result after multiplication becomes in opposite direction. Whereas the value of the product vector becomes zero if value of λ is 0.