Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Multiple Choice Question, question 10.

Provide solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Multiple Choice Question, question 10.

Answers (1)

Final Answer:

(a) \left [\frac{19}{8},\frac{57}{16},\frac{17}{16} \right ]

Hint: Bisection divides triangle in ratios

\frac{AB}{AC}=\frac{BD}{DC}

Given: A(3,2,0), B(5,3,2) and C(-9,6,-3) are vertices of triangle ABC

To find: Point D coordinates which meets BC at bisector of \angle BAC

Solution:  

  

As bisector AD meets BC at D, therefore

\Rightarrow \frac{AB}{AC}=\frac{BD}{DC}

Using distance formula

\begin{aligned} &A B=\sqrt{(5-3)^{2}+(3-2)^{2}+(2-0)^{2}} \\ &=\sqrt{4+1+4} \\ &=\sqrt{9} \\ &=3 \end{aligned}

and,

\begin{aligned} &A C=\sqrt{(-9-3)^{2}+(6-2)^{2}+(-3-0)^{2}} \\ &=\sqrt{(-12)^{2}+4^{2}+3^{2}} \\ &=\sqrt{144+16+9} \\ &=\sqrt{169} \\ &=13 \end{aligned}

Therefore,

\frac{BD}{DC}=\frac{13}{8}

D divides BC in the ratio 3:13 internally

Using section formula coordinates of D are

\begin{aligned} &(x, y, z)=\left[\Rightarrow \frac{-9 \times 3+5 \times 13}{3+13}, \frac{6 \times 3+13 \times 3}{3+13}, \frac{-3 \times 3+13 \times 2}{3+13}\right] \\ &(x, y, z)=\left[\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right] \end{aligned}

Hence coordinate of D are

\left [\frac{19}{8},\frac{57}{16},\frac{17}{16} \right ]

Therefore option (a) is correct

Posted by

infoexpert24

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question