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Question

Mathematics Question on Straight lines

Find the angle between two vectors (a→=2i^+j^−3k^) and (b→=3i^−2j^−k^).

A

(A) −160∘

B

(B) −60∘

C

(C) 160∘

D

(D) 60∘

Answer

(D) 60∘

Explanation

Solution

Explanation:
Given:a→=2i^+j^−3k^ and b→=3i^−2j^−k^a→⋅b→=(2i^+j^−3k^)(3i^−2j^−k^)=6−2+3=7….(1)|a→|=22+12+(−3)2=14…(2)|b→|=32+(−2)2+(−1)2=14….(3)cos⁡θ=a→⋅b→|a→|⋅|b→|Put the values from (1), (2) amnd (3) in above equation:=714.14=12cos⁡θ=cos⁡60∘θ=60∘Hence, the correct option is (D).