Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

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11th Andhra Pradesh Board

IMPORTANT

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Find the angle between the lines whose direction cosines satisfy the equations $l + m + n = 0, l^{2} + m^{2} - n^{2} = 0$ .

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Important Questions on Direction Cosines and Direction Ratios

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

If a ray makes angles

α, β, γ, δ

with the four diagonals of a cube find

\cos^{2} α + \cos^{2} β + \cos^{2} γ + \cos^{2} δ

.

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

If

(l_{1}, m_{1}, n_{1}), (l_{2}, m_{2}, n_{2})

are direction cosines of two intersecting lines, show that direction cosines of two lines bisecting the angles between them are proportional to

(l_{1} \pm l_{2}, m_{1} \pm m_{2}, n_{1} \pm n_{2})

.

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

A (- 1, 2, - 3), B (5, 0, - 6), C (0, 4, - 1)

are three points. Show that the direction cosines of the bisectors of

∠ B A C

are proportional to

(25, 8, 5)

and

(- 11, 20, 23)

.

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

If

(6, 10, 10), (1, 0, - 5), (6, - 10, 0)

are vertices of a triangle, find the direction ratios of its sides. Determine whether it is right angled or isosceles.

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

The vertices of a triangle are

A (1, 4, 2), B (- 2, 1, 2), C (2, 3, - 4) .

Find

∠ A, ∠ B, ∠ C

.

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11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

Find the angle between the lines whose direction cosines are given by the equations

3 l + m + 5 n = 0

and

6 m n - 2 n l + 5 l m = 0

.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 6 - Direction Cosines and Direction Ratios>Exercise 6(b)>Q III

If a variable line in two adjacent positions has direction cosines

(l, m, n)

and

(l + δ l, m + δ m, n + δ n)

, show that the small angle

δ θ

between the two positions is given by

(δ θ)^{2} = (δ l)^{2} + (δ m)^{2} + (δ n)^{2}

.