Prove that /\ |[a+bx, c+dx, p+qx],[-ax+...

Prove that ` /_\ |[a+bx, c+dx, p+qx],[-ax+b, cx+d, px+q],[u,v,w]|=(1-x^2) [[a,c,p],[b,d,q],[u,v,w]] `

`0`

`1-x^(2)`

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Prove that d/(dx)|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_3,v_3,w_3)|=|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_4,v_4,w_4)| where u,v,w are functions of x and (du)/(dx)=u_1,(d^2u)/(dx^2)=u_2, etc.

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If hat u , hat v , hat w be three non-coplanar unit vectors with angles between hat u& hat v is alpha between hat v& hat w is beta and between hat w& hat u is gamma . If vec a , vec b , vec c are the unit vectors along angle bisectors of alpha,beta,gamma respectively, then prove that [ vec ax vec b vec bx vec c vec cx vec a]=1/(16)[ hat u hat v hat w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2)

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MCGROW HILL PUBLICATION-DETERMINANTS-EXERCISE (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)

If a,b,c are non zero real numbers then Delta=|(1,ab,1/a+1/b),(1,bc,...
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If a,b,c gt1 then Delta=|(log(a)(abc),log(a)b,log(a)c),(logb(abc),1,lo...
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Prove that /\ |[a+bx, c+dx, p+qx],[-ax+b, cx+d, px+q],[u,v,w]|=(1-x^2...
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Let Delta=|(1,sin theta, 1),(-sin theta, 1, sin theta),(-1,-sin theta,...
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The determinat Delta=|(b^2-ab,b-c,bc-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-...
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If |{:(6i,-3i,1),(4,3i,1),(20,3,i):}|=x+iy,i=sqrt(-1) then
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The number of distinct real roots of |s in x cos x cos x cos x s in x ...
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if omega!=1 is a complex cube root of unity, and x+iy=|[1,i,-omega],[-...
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If e^(lx)=cosx+isinx and x+iy=|(1,e^(pi i//4),e^(pi i//3)),(e^(-pi i...
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If a,b,c,in R, find the number of real root of the equation |{:(x,c,-b...
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If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),x,x):}| =3 then the value of |{:(...
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If Delta=|(sin alpha, cos alpha, sin alpha+cos beta),(sin beta, cos al...
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Suppose a,b,c epsilon R and a,b,c gt 0. Let Delta=|(loga, logb, logc...
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The value of theta , lying between theta =0 and theta=(pi)/(2) and ...
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Solve |{:(x^(2)-1,,x^(2)+2x+1,,2x^(2)+3x+1),(2x^(2)+x-1,,2x^(2)+5x-3,,...
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If a(r)="cos"(2rpi)/9+i "sin"(2rpi)/9 then value of the determinant ...
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If a!=p,b!=q,c!=r and the system of equations px+by+cz=0 ax+qy+cz=...
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For a fixed positive integer n if D= |(n!, (n+1)!, (n+2)!),((n+1)!, (n...
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If a, b, c are in A.P., and Delta=|[x+2,x+7,a],[x+5,x+11,b],[x+8,x+15,...
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If Delta=|(1+y,1-y,1-y),(1-y,1+y,1-y),(1-y,1-y,1+y)|=0, then value of ...
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