SATHEE: 3D Geometry 1 Question 1

3D Geometry 1 Question 1

1. The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ , is

(a) $\frac{π}{3}$

(b) $\frac{π}{4}$

(d) $\frac{π}{2}$

(2014 Main)

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Answer:

Correct Answer: 1. (a)

Solution:

We know that, angle between two lines is

$\cos θ = \frac{a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$

$l + m + n + q = 0$

$\Rightarrow l = - (m + n) \Rightarrow (m + n)^{2} = l^{2}$

$\Rightarrow m^{2} + n^{2} + 2 m n = m^{2} + n^{2} [∵ l^{2} = m^{2} + n^{2}, given]$

$2 m n = 0$

$When m = 0$

$\Rightarrow l = - n$

Hence, $(l, m, n)$ is $(1, 0, - 1)$ .

When $n = 0$ , then $l = - m$

Hence, $(l, m, n)$ is $(1, 0, - 1)$ .

$∴ \cos θ = \frac{1 + 0 + 0}{\sqrt{2} \times \sqrt{2}} = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

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3D Geometry 1 Question 1

1. The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ , is

Answer:

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

3D Geometry 1 Question 1

1. The angle between the lines whose direction cosines satisfy the equations l+m+n=0 and l2=m2+n2, is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ , is