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 Direction Cosines and Direction Ratios exercise Fill in the blanks question 14

Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 14

Answers (1)

Final Answer:  \frac{\pi }{3}

Hint:

Dot product of two direction cosine two vectors

Given:

\begin{aligned} &\left(a_{1}, b_{1}, c_{1}\right)=(1,1,2) \text { and } \\ &\left(a_{2}, b_{2}, c_{2}\right)=(\sqrt{3}-1,-\sqrt{3}-1,4) \end{aligned}

To Find: 

Angle between two vectors

Solution:

Angle between two vectors with direction ratios \left(a, b, c_{1}\right) \text { and }\left(a_{2}, b_{2}, c_{2}\right)  is
given by

\cos \theta=\left[\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \cdot \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\right]

\text { Now, } \sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}=\sqrt{(1)^{2}+(1)^{2}+(2)^{2}}=\sqrt{1+1+4}=\sqrt{6}

\text { Also } \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}=\sqrt{(\sqrt{3}-1)^{2}+(-\sqrt{3}-1)^{2}+4^{2}}

                                      =\sqrt{3+1-2 \sqrt{3}+3+1+2 \sqrt{3}+16}=\sqrt{24}

\text { Hence } \cos \theta=\left[\frac{1(\sqrt{3}-1)+1 \cdot(-\sqrt{3}-1)+2 \cdot 4}{\sqrt{6} \cdot \sqrt{24}}\right]

\begin{aligned} &\cos \theta=\left[\frac{\sqrt{3}-1-\sqrt{3}-1+8}{\sqrt{6 \times 24}}\right] \\ &\cos \theta=\frac{6}{12} \end{aligned}

\begin{aligned} &\theta=\cos ^{-1}\left[\frac{1}{2}\right] \\ &\theta=\frac{\pi}{3} \end{aligned}

Therefore, the angle between two vectors is \frac{\pi }{3}

Posted by

infoexpert26

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