Let a, b and c be non-zero vectors such that (a×b)×c=1/3|b||c|a. If θ is the acute angle between the vectors b and c, then θ equals - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

1 attempts0% success rate3 marks (−1)

Let a, b and c be non-zero vectors such that (a \times b) \times c = \frac{1}{3} ∣ b ∣∣ c ∣ a . If θ is the acute angle between the vectors b and c, then sin θ equals

Solution & Step-by-step Explanation

Using the vector triple product formula (a \times b) \times c = (a \cdot c) b - (b \cdot c) a . The given equation is (a \cdot c) b - (b \cdot c) a = \frac{1}{3} ∣ b ∣∣ c ∣ a . Rearranging: (a \cdot c) b = (b \cdot c + \frac{1}{3} ∣ b ∣∣ c ∣) a . Since a and b are non-collinear, their coefficients must be zero: a \cdot c = 0 . b \cdot c + \frac{1}{3} ∣ b ∣∣ c ∣ [c i t e_{s} t a r t] = 0 . ∣ b ∣∣ c ∣ cos θ = - \frac{1}{3} ∣ b ∣∣ c ∣ cos θ = - 1/3 . sin^{2} θ = 1 - cos^{2} θ = 1 - (- 1/3)^{2} = 1 - 1/9 = 8/9 . sin θ = 8/9 = \frac{2 2}{3} .

Try it yourself before checking the explanation above.

Let a, b and c be non-zero vectors such that (a \times b) \times c = \frac{1}{3} ∣ b ∣∣ c ∣ a . If θ is the acute angle between the vectors b and c, then sin θ equals

\frac{1}{3}

\frac{2}{3}

\frac{2}{3}

\frac{2 2}{3}

Practice with timed mock tests and track your performance across Mathematics.