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Class 12 Vector Algebra · Assertion Reason1 Marksdot_product_angle

Class 12 Maths · Vector Algebra · Assertion Reason #32

Assertion (A): The cosine of the angle between (2,2,−1) and (6,−3,2) is 16/21. Reason (R): For nonzero vectors a,b, cos θ = (a · b)/(|a||b|).

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true but R is false.
(D) A is false but R is true.

✅ Step-by-Step Solution

Final Answer: Option (D): A is false but R is true.

The dot product is 12 − 6 − 2 = 4, and the norms are 3 and 7. Thus cos θ = 4/21, not 16/21.

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