Maths-
General
Easy
Question
Let OPQR is a tetrahedron such that O is origin and
are position vectors of P, Q, R respectively and a is the angle which OP makes with face PQR then
- 1
- 2
- tana =
- none of these
The correct answer is: 2
To find the angle made by OP with face PQR
It is given that OP=p
OQ=q
OR=r
PQR=(OQ-OP) X(OR-OQ)=(q-p)X(r-q)
Angle= ![cos left parenthesis theta right parenthesis equals 2 left parenthesis q minus p right parenthesis X left parenthesis r minus q right parenthesis divided by left parenthesis q minus p right parenthesis left parenthesis r minus q right parenthesis
equals 2](data:image/png;base64,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)
Hence required angle is 2.
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