Andhra Pradesh Board Solutions for Chapter: Direction Cosines and Direction Ratios, Exercise 2: Exercise 6(b)

Author:Andhra Pradesh Board

Andhra Pradesh Board Mathematics Solutions for Exercise - Andhra Pradesh Board Solutions for Chapter: Direction Cosines and Direction Ratios, Exercise 2: Exercise 6(b)

Attempt the practice questions on Chapter 6: Direction Cosines and Direction Ratios, Exercise 2: Exercise 6(b) with hints and solutions to strengthen your understanding. Intermediate First Year Mathematics Paper 1B solutions are prepared by Experienced Embibe Experts.

Questions from Andhra Pradesh Board Solutions for Chapter: Direction Cosines and Direction Ratios, Exercise 2: Exercise 6(b) with Hints & Solutions

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

Find the angle between the lines whose direction cosines satisfy the equations l+m+n=0, l2+m2-n2=0.

HARD
11th Andhra Pradesh Board
IMPORTANT

If a ray makes angles α, β, γ, δ with the four diagonals of a cube find cos2α+cos2β+cos2γ+cos2δ.

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

If l1,m1,n1, l2,m2,n2 are direction cosines of two intersecting lines, show that direction cosines of two lines bisecting the angles between them are proportional to l1±l2,m1±m2,n1±n2.

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

A(-1,2,-3), B(5,0,-6), C(0,4,-1)  are three points. Show that the direction cosines of the bisectors of BAC are proportional to (25,8,5) and (-11,20,23).

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

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.

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

The vertices of a triangle are A(1,4,2), B(-2,1,2), C(2,3,-4). Find A, B, C.

HARD
11th Andhra Pradesh Board
IMPORTANT

Find the angle between the lines whose direction cosines are given by the equations 3l+m+5n=0 and 6mn-2nl+5lm=0.

MEDIUM
11th Andhra Pradesh Board
IMPORTANT

If a variable line in two adjacent positions has direction cosines (l, m, n) and (l+δl,m+δm,n+δn), show that the small angle δθ between the two positions is given by (δθ)2=(δl)2+(δm)2+(δn)2.