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The plane which can be formed with the v...

The plane which can be formed with the vectors `overline a=3overline i-4overline j+2overline k,overline b=2overline i-overline j+6overline k,overline c=5overline i-5overline j+4overline k`,is.

A

Quadrilateral

B

Triangle

C

Circle

D

Hyperbola

Text Solution

Verified by Experts

The correct Answer is:
B
`hat a+hatb+hatc=hat0("triangle law")`
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[[overline(a)-overline(b), overline(b)-overline(c), overline(c)-overline(a)]]=

[[overline(a), overline(b)+overline(c), overline(c)+overline(b)+overline(a)]]=

If overline(a), overline(b), overline(c) are non-coplanar vectors and the vectors overline(p)=-overline(a)+3overline(b)-5overline(c), overline(q)= -overline(a)+overline(b)+overline(c) and overline(r)= 2overline(a)-3overline(b)+overline(c) are coplanar such that overline(p)=moverline(q)+noverline(r) , then

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|[overline(a)*overline(a), overline(a)*overline(b)], [overline(a)*overline(b), overline(b)*overline(b)]|=

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