A tetrahedron has vertices at O (0, 0, 0) , A (1,2,1), B (2,1,3) and C (-1,1,2). Then the angle between the faces OAB and ABC will be 

  • Option 1)

    \cos ^{-1}(17/31)\;

  • Option 2)

    \; 30^{\circ}\;

  • Option 3)

    \; 90^{\circ}\;

  • Option 4)

    \; \cos ^{-1}(19/35)\;

 

Answers (1)

As we learnt in

Ange between two lines in terms of direction cosines and direction ratios -

If two lines having direction ratios a1,b1,c1 and a2,b2,c2 then the angle between them is given by

\cos \Theta = \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a{_{1}}^{2}+b{_{1}}^{2}+c{_{1}}^{2}}\sqrt{a{_{2}}^{2}+b{_{2}}^{2}+c{_{2}}^{2}}}

If two lines have direction ratios as l1,m1,n1 and l2,m2,n2 then the angle betwee them is given by

\cos \Theta = l_{1}l_{2}+m_{1}m_{2}+n_{1}n_{2}
 

 

-

 

 Vector perpendicular to face OAB= \vec{OA}\times \vec{OB}

= 5\hat{i}- \hat{j}-3\hat{k}

Similarily, vector perpendicular to face ABC= = \hat{i}- 5\hat{j}-3\hat{k}

Angle between faces

\cos \theta= \left | \frac{5+5+9}{\sqrt{35}\sqrt{35}} \right |= \frac{19}{35}

(Using dot product)

 


Option 1)

\cos ^{-1}(17/31)\;

Incorrect option

Option 2)

\; 30^{\circ}\;

Incorrect option

Option 3)

\; 90^{\circ}\;

Incorrect option

Option 4)

\; \cos ^{-1}(19/35)\;

Correct option

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions