Home
Class 12
MATHS
If OABC be a regular tetrahedron such ...

If OABC be a regular tetrahedron such that `OA^(2) + BC^(2) = OB^(2) + CA^(2) = OC^(2) + AB^(2)` then _

A

OA is perpendicular on BC

B

OB is perpendicular on CA

C

OC is perpendicular on AB

D

AB is perpendicular on BC

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (B Integer Answer Type)|5 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (C Matrix Match Type)|2 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Short Answer Type Questions|26 Videos

  • INTEGRATION BY PARTS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|6 Videos

Similar Questions

Explore conceptually related problems

‘O’ is any point in the interior of a triangle ABC. If OD bot BC, OE bot AC and OF bot AB, show that (i) OA^(2) + OB^(2) + OC^(2) - OD^(2) - OE^(2) - OF^(2) = AF^(2) + BD^(2) + CE^(2) (ii) AF^(2) + BD^(2) + CE^(2) = AE^(2) + CD^(2) + BE^(2) .

O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB^(2) + OD^(2)

‘O’ is any point inside a rectangle ABCD. Prove that OB^(2) + OD^(2) = OA^(2) + OC^(2)

ABC is an equilateral triangle. AD is perpendicular to BC. Prove that AB^(2) + BC^(2) + CA^(2) =4AD^(2)

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

In Delta ABC , AD is a median and AM _|_ BC.Prove that (a) AC^(2) = AD^(2) +BC.DM+ ((BC)/(2))^(2) (b) AB^(2) = AD^(2) -BC.DM+ ((BC)/(2))^(2) (c ) AC^(2) + AB^(2) = 2AD^(2) +(1)/(2) BC^(2)

Prove that bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2) = s^(2)

If E is a point on side CA of an equilateral triangle ABC such that BE bot CA , then AB^2 + BC^2 + CA^2 is equal to___

If a + b +c =9 and ab + bc + ca =26, then find a ^(2) + b ^(2) + c ^(2).

D,E,F are the mid - points of the sides overline(BC),overline(CA)andoverline(AB) respectively of the triangle ABC , using coordinate geometry show that , 3(BC^(2)+CA^(2)+AB^(2))=4(AD^(2)+BE^(2)+CF^(2)) .

Home
Profile