Home
Class 12
MATHS
If OABC is a tetrahedron such thatOA^2 +...

If OABC is a tetrahedron such that`OA^2 + BC^2 = OB^2 + CA^2 = OC^2 + AB^2` then

A

`OA bot BC`

B

`OB bot AC`

C

`OC bot AB`

D

`AB bot AC`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `vec(OA)=veca,vec(OB)=vecb,vec(OC)=vecc`
Then from the given conditions.
`veca.veca+(vecb-vecc).(vecb-vecc)=vecb.vecb+(vecc-veca).(vecc-veca)`
`rArr -2vecb.vecc=-2vecc.veca`
`rArr vecc.(vecb-veca)=0`
`rArr ar(trianglePQR)=1/2xx 4 xx 4=8`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

  • ELLIPSE

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

In the figure given below, AOBA is the part of the ellipse 9x^(2) + y^(2) = 36 in the first quadrant such that OA = 2 and OB = 6. Find the area between arc AB and the chord AB

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=

If 'O' is any point in the interior of rectangle ABCD, then prove that : OB^(2) + OD^(2) = OA^(2) + OC^(2)

The perpendicular from A on side BC at a Delta ABC intersects BC at D such that DB=3 CD. Prove that 2 AB^(2)=2AC^(2)+BC^(2)

In AD bot BC , prove that AB^(2)+CD^(2)=BD^(2)+AC^(2)

In the given fig. if AD bot BC Prove that AB^(2) + CD^(2) = BD^(2) + AC^(2) .

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

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

In a tetrahedron OABC, the edges are of lengths, |OA|=|BC|=a,|OB|=|AC|=b,|OC|=|AB|=c. Let G_1 and G_2 be the centroids of the triangle ABC and AOC such that OG_1 _|_ BG_2, then the value of (a^2+c^2)/b^2 is