Home
Class 11
MATHS
|(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1)|...

`|(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1)|=`

A

`|{:(1,b,c),(x,y,z),(yz,zx,xy):}|`

B

`|{:(a,b,c),(x,y,z),(y,z,x):}|`

C

`|{:(ax,by,cz),(a^(2),b^(2),x^(2)),(1,1,1):}|`

D

`|{:(x,y,z),(a,b,c),(yz,zx,xy):}|`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - II|52 Videos

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS-PRACTICE EXERCISE|39 Videos

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -PRACTICE EXERCISE|41 Videos

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

Without expanding the determinant, prove that (i) |{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}| (ii) |{:(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}| (iii) |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

Prove that |{:((1+ax)^(2),(1+ay)^(2),(1+az)^(2)),((1+bx)^(2),(1+by)^(2),(1+bz)^(2)),((1+cx)^(2),(1+cy)^(2),(1+cz)^(2)):}|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x) .

|(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(2))|=0,x!=y!=zimplies1+xyz=

Find the coordinates of the centroid fof the triangle whose vertices are (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3))

Assertion (A): A(x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) . The projection of AB on the line with D.C's (l,m,n) is l(x_(2)-x_(1)) +m(y_(2)-y_(1))+n(z_(2)-z_(1)) Reason (R ) : The projection of the join of A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) on yz plane is sqrt((y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2))

A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) are two points. Then the lenghts of projection on

If [(x-1,2,y-5),(z,0,2),(1,-1,1+a)]=[(1-x,2,-y),(2,0,2),(1,-1,1)] then find the values of x,y,z and a.

Prove that the line segment joining (x_(1),y_(1),z_(1)) and (x_(2),y_(2),z_(2)) is divided by XY,YZ,ZX-plalnes respectively in the ratio -z_(1) : z_(2),-x_(1) :x_(2),-y_(1) : y_(2) .

A point P moves on the fixed plane (x)/(a)+(y)/(b)+(z)/(c )=1 the plane through the point P and perpendicular to the line bar(OP) where O=(0,0,0) meets coordinate axes in A, B, C. Show that the locus of the point of intersection of the planes through A, B, C and parallel to the cooridnate planes is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(ax)+(1)/(by)+(1)/(cz) .