Maths · Vectors and 3-D geometry · chapter 10 of 13

Class 12 Maths Chapter 10: Vector Algebra Assertion-reason questions with answers

2 assertion-reason questions on Vector Algebra, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The vectors −2→a and 5→a, where →a ≠ →0, are collinear. Reason (R): Collinear vectors always have the same direction.
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Answer: (c) A is true, but R is false.

Both are scalar multiples of →a, so both are parallel to the line of →a: A is true. Collinear vectors may point in opposite directions (−2→a and 5→a do), so R is false.

Question 2
Assertion (A): The vectors î + 2ĵ − k̂ and 3î − ĵ + k̂ are perpendicular. Reason (R): For non-zero vectors →a and →b, →a · →b = 0 if and only if →a and →b are perpendicular.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

(1)(3) + (2)(−1) + (−1)(1) = 0, and both vectors are non-zero, so by R they are perpendicular. A and R are true and R explains A.

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