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Latus Rectum

If the angle ...

Question

If the angle between $¯ a = λ^i + 3^j - k, ¯ b = 2 λ^i + λ^j - k$ , is acute and $¯ b$ makes obtuse angle with the axes of its coordinates, then $λ \in$ ___

(- \infty, 0)

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(- \infty, \frac{1}{2})

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(- \infty, \frac{1}{2})

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(1, \infty)

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Solution

The correct option is A $(- \infty, 0)$

$¯ a . ¯ b > 0 \Rightarrow 2 λ^{2} - 3 λ + 1 > 0 \Rightarrow λ < \frac{1}{2}$ or $λ > 1 . . . . (1)$
$¯ b . i < 0, ¯ b . j < 0, ¯ b . k < 0 \Rightarrow λ < 0 . . . . (2)$
Form (1)and (2), $λ \in (- \infty, 0)$

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If the angle between ¯a=λ^i+3^j−k,¯b=2λ^i+λ^j−k, is acute and ¯b makes obtuse angle with the axes of its coordinates, then λ∈___

The correct option is A (−∞,0) ¯a.¯b>0⇒2λ2−3λ+1>0⇒λ<12 or λ>1....(1) ¯b.i<0,¯b.j<0,¯b.k<0⇒λ<0....(2) Form (1)and (2), λ∈(−∞,0)

If the angle between $¯ a = λ^i + 3^j - k, ¯ b = 2 λ^i + λ^j - k$ , is acute and $¯ b$ makes obtuse angle with the axes of its coordinates, then $λ \in$ ___

The correct option is A $(- \infty, 0)$

$¯ a . ¯ b > 0 \Rightarrow 2 λ^{2} - 3 λ + 1 > 0 \Rightarrow λ < \frac{1}{2}$ or $λ > 1 . . . . (1)$
$¯ b . i < 0, ¯ b . j < 0, ¯ b . k < 0 \Rightarrow λ < 0 . . . . (2)$
Form (1)and (2), $λ \in (- \infty, 0)$