Test Index

NCERT Class XII Mathematics Chapter - - Solutions

© examsnet.com
Question : 5 of 78
Marks: +1, -0
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, – 4), (–1, 1, 2) and (–5, – 5, –2)
Solution:  
Let the vertices of the triangle be A, B and C respectively.
Here, ∣AB∣=(−1−3)2+(1−5)2+(2+4)2\left|AB\right|=\sqrt{(-1-3)^2+(1-5)^2+(2+4)^2} =217=2\sqrt{17}
∣BC∣=(−5+1)2+(−5−1)2+(−2−2)2\left|BC\right|=\sqrt{(-5+1)^2+(-5-1)^2+(-2-2)^2} =217=2\sqrt{17}
∣CA∣=(3+5)2+(5+5)2+(−4+2)2\left|CA\right|=\sqrt{(3+5)^2+(5+5)^2+(-4+2)^2} =242=2\sqrt{42}
∴ d.c. of AB are ⟨−1−3∣AB∣,1−5∣AB∣,2+4∣AB∣⟩\langle \frac{-1-3}{\left|AB\right|}, \frac{1-5}{\left|AB\right|}, \frac{2+4}{\left|AB\right|} \rangle i.e., ⟨−217,−217,317⟩\langle \frac{-2}{\sqrt{17}}, \frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}} \rangle
∴ d.c. of AB are ⟨−5+1∣BC∣,−5−1∣BC∣,−2−2∣BC∣⟩\langle \frac{-5+1}{\left|BC\right|}, \frac{-5-1}{\left|BC\right|}, \frac{-2-2}{\left|BC\right|} \rangle i.e., ⟨−217,−317,−217⟩\langle \frac{-2}{\sqrt{17}}, \frac{-3}{\sqrt{17}}, \frac{-2}{\sqrt{17}} \rangle
∴ d.c. of AB are ⟨3+5∣CA∣,5+5∣CA∣,−4+2∣CA∣⟩\langle \frac{3+5}{\left|CA\right|}, \frac{5+5}{\left|CA\right|}, \frac{-4+2}{\left|CA\right|} \rangle i.e., ⟨442,542,−142⟩\langle \frac{4}{\sqrt{42}}, \frac{5}{\sqrt{42}}, \frac{-1}{\sqrt{42}} \rangle
© examsnet.com
Go to Question:
Prev Question
Next Question