99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

The angle between the vectors 2 k ^ - 3 j ^ and i ^ - 2 k ^ is

Options

Acos - 1 8 65
Bcos - 1 - 4 65
Ccos - 1 2 65
Dcos - 1 3 13

Correct answer

B. cos - 1 - 4 65

Step-by-step solution

Given Vectors are 2 k ^ - 3 j ^       &     i ^ - 2 k ^ Now, For a →   &   b → their dot product is a → . b → = a → b → cosθ ⇒ cos θ = a → . b → a → b → ∴ cos θ = 2 k ^ - 3 j ^ . i ^ - 2 k ^ 2 k ^ - 3 j ^ i ^ - 2 k ^ = - 4 2 2 + - 3 2 × 1 2 + - 2 2 ⇒ cos θ = - 4 65 ⇒ θ = cos - 1 - 4 65

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