If a-b-care three vectors such that -a-3- -b-1 and -c-2 and -b-c-3 and b-3c-a- then the possible value of - is where - denotes greatest integer function

|b×c|=|b||c|sinθ |b||c|sinθ=√(3) 1×2×sinθ=√(3) sinθ=√(3)2 (1) Now b 3c=λa Squaring both sides nbsp; (b 3c)^2=(λa)^2 |b|^2 6(b·c)+9|c|^2=λ^2|a|^2 |b|^2 6| ...

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Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

If a,b,care t...

Question

If $\to a, \to b, \to c$ are three vectors such that $| \to a | = 3$ , $| \to b | = 1$ and $| \to c | = 2$ and $| \to b \times \to c | = \sqrt{3}$ and $\to b - 3 \to c = λ \to a$ , then the possible value of $[λ]$ is (where $[.]$ denotes greatest integer function)

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Solution

The correct option is C $3$
$| \to b \times \to c | = | \to b | | \to c | sin θ$
$| \to b | | \to c | sin θ = \sqrt{3}$
$1 \times 2 \times sin θ = \sqrt{3}$
$sin θ = \frac{\sqrt{3}}{2} - (1)$
Now
$\to b - 3 \to c = λ \to a$
Squaring both sides
$(\to b - 3 \to c)^{2} = (λ \to a)^{2}$
$| \to b |^{2} - 6 (\to b \cdot \to c) + 9 | \to c |^{2} = λ^{2} | \to a |^{2}$
$| \to b |^{2} - 6 | \to b | | \to c | cos θ + 9 | \to c |^{2} = λ^{2} | \to a |^{2}$
$1^{2} - 6 \times 1 \times 2 \times \frac{1}{2} + 9 (2)^{2} = 9 λ^{2}$
$λ = \pm \frac{31}{9}$
$[λ] = 3$ or $[λ] = - 4$

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If →a,→b,→care three vectors such that |→a|=3, |→b|=1 and |→c|=2 and |→b×→c|=√3 and →b−3→c=λ→a, then the possible value of [λ] is (where [.] denotes greatest integer function)

If $\to a, \to b, \to c$ are three vectors such that $| \to a | = 3$ , $| \to b | = 1$ and $| \to c | = 2$ and $| \to b \times \to c | = \sqrt{3}$ and $\to b - 3 \to c = λ \to a$ , then the possible value of $[λ]$ is (where $[.]$ denotes greatest integer function)