A plane passes through a fixed point `(a ,b ,c)dot` The locus of the foot of the perpendicular to it from the origin is a sphere of radius a. `1/2sqrt(a^2+b^2+c^2)` b. `sqrt(a^2+b^2+c^2)` c. `a^2+b^2+c^2` d. `1/2(a^2+b^2+c^2)`

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then (a) 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b and c on the O X ,O Ya n dO Z axes. The area of triangle A B C is a. 1/2(a b+b c+c a) b. 1/2a b c(a+b+c) c. 1/2(a^2b^2+b^2c^2+c^2a^2)^(1//2) d. 1/2(a+b+c)^2

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : costheta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,c and a^prime ,b^(prime),c ' from the origin, then a. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0 b. 1/(a^2)-1/(b^2)-1/(c^2)+1/(a^('2))-1/(b^('2))-1/(c^('2))=0 c. 1/(a^2)+1/(b^2)+1/(c^2)-1/(a^('2))-1/(b^('2))-1/(c^('2))=0 d. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0

Prove the identities: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

In triangle ABC , a (b^2 +c^2 ) cos A + b (c^2 +a^2 ) cos B + c(a^2 +b^2 ) cos C is equal to