SATHEE: Straight Line and Pair of Straight Lines 2 Question 2

Straight Line and Pair of Straight Lines 2 Question 2

2. Consider three points

$P = - \sin (β - α) - \cos β, Q = \cos (β - α), \sin β$

and $R = \cos (β - α + θ) \sin (β - θ)$ ,

where $0 < α, β, θ < \frac{π}{4}$ . Then,

$(2008, 4 M)$

(a) $P$ lies on the line segment $R Q$

(b) $Q$ lies on the line segment $P R$

(d) $P, Q, R$ are non-colinear

Show Answer

Answer:

Correct Answer: 2. (d)

Solution:

For collinear points

$Δ = | \begin{array}{ccc} - \sin (β - α) & - \cos β & 1 \\ \cos (β - α) & \sin β & 1 \\ \cos (β - α + θ) & \sin (β - θ) & 1 \end{array} |$

Clearly, $Δ \neq 0$ for any value of $α, β, θ$ .

Hence, points are non-collinear.

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Straight Line and Pair of Straight Lines 2 Question 2

2. Consider three points

Answer:

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