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JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Vector Algebra

If

∣ a ∣ = 2, ∣ b ∣ = 5

and

∣ a \times b ∣ = 8

, then

∣ a \cdot b ∣

is equal to :

(A)5
(B)4
(C)6✓ Correct
(D)3

Answer: (C)

Solution

Using the vector identities:

∣ a \times b ∣ = ∣ a ∣∣ b ∣ sin θ = 8

∣ a \cdot b ∣ = ∣ a ∣∣ b ∣∣ cos θ ∣

From the first equation:

2 \cdot 5 \cdot sin θ = 8

sin θ = \frac{8}{10} = \frac{4}{5}

Using

sin^{2} θ + cos^{2} θ = 1

:

cos^{2} θ = 1 - \frac{16}{25} = \frac{9}{25}

∣ cos θ ∣ = \frac{3}{5}

Therefore:

∣ a \cdot b ∣ = 2 \cdot 5 \cdot \frac{3}{5} = 6

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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