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The angle between the straight lines \( \Large x-y\sqrt{3}=5\ and\ \sqrt{3}x+y=7 \) is:

A) \( \Large 90 ^{\circ} \)
B) \( \Large 60 ^{\circ} \)
C) \( \Large 75 ^{\circ} \)
D) \( \Large 30 ^{\circ} \)

Correct Answer:


B) \( \Large 60 ^{\circ} \)

Description for Correct answer:

Given equation is compared with \( \Large a_{1}x+b_{1}y=0\ and\ a_{2}x+b_{2}y=0 \)

Now, \( \Large a_{1}a_{2}+b_{1}b_{2}= \left(1\right) \left(\sqrt{3}\right)+ \left(-\sqrt{3}\right) \left(1\right)=0 \)

Line are perpendicular

\( \Large \theta-90 ^{\circ} \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines

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Similar Questions

1). The three straight lines \( \Large ax+by=c,\ bx+cy=a\ and\ cx+ay=b \) are collinear if:

A). \( \Large a+b+c = 0 \)

B). \( \Large c+a=b \)

C). \( \Large b+c=a \)

D). \( \Large a+b=c \)

2). If a tangent to the curve \( \Large y=6x-x^{2} \) is parallel to the line \( \Large 4x-2y-1=0 \) then the point of tangency on the curve is: ' _

A). (6, 1)

B). (8, 2)

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3). Distance between the lines \( \Large 5x+3y-7=0\ and\ 15x+9y+14=0 \) is:

A). \( \Large \frac{35}{\sqrt{34}} \)

B). \( \Large \frac{1}{\sqrt{34}} \)

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D). \( \Large \frac{35}{3\sqrt{34}} \)

4). The equation of the sides of a triangle are \( \Large x-3y=0.\ 4x+3y=5\ and\ 3x+y=0 \). The lines \( \Large 3x-4y=0 \) passage through

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B). the centroid

C). the orthocentre

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5). If (-4, -5) is one vertex and \( \Large 7x-y+8=0 \) is one diagonal of a square then the equation of second diagonal is:

A). \( \Large x+3y=21 \)

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6). The number of the straight which is equally inclined to both the axes is

A). 4

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7). The line passing. through \( \Large \left(1-\frac{ \pi }{2}\right) \) and perpendicular to \( \Large \sqrt{3} \sin \theta + 2\cos \theta =\frac{4}{r} \), is:

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B). \( \Large 5=2\sqrt{3}r\sin \theta +4r\cos \theta \)

C). \( \Large 2=\sqrt{3}r\cos \theta + 2r\sin \theta \)

D). \( \Large 5=2\sqrt{3}r\sin \theta + 4r\cos \theta \)

8). If the straight line \( \Large ax+by+c=0 \) always passes through \( \Large \left(1-2\right) \) then abc are

A). in AP

B). in HP

C). in GP

D). none of these

9). Two points A and B have co-ordinates (1, 1) and (3, -2) respectively. The co-ordinates of a point distant \( \Large \sqrt{85} \) from B on the line through B perpendicular to AB are:

A). (5, 7)

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A). \( \Large x^{2}+ \left(3-x^{2}\right)=9 \)

B). \( \Large \left(3+y\right)^{2}+y^{2}=9 \)

C). \( \Large xy=0 \)

D). \( \Large \left(x-y\right)^{2}=9 \)