Let ` vec a_r=x_r hat i+y_r hat j+z_r hat k ,r=1,2,3` be three mutually perpendicular unit vectors, then the value of `|[x_1,x_2,x_3],[y_1,y_2,y_3],[z_1,z_2,z_3]|` is equal to a. `0` b. `+-1` c. `+-2` d. none of these

Let overset(to)(a_(r))=x_(r )hat(i)+y_(r )hat(j)+z_(r )hat(k),r=1,2,3 three mutually prependicular unit vectors then the value of |{:(x_(1),,x_(2),,x_(3)),(y_(1),,y_(2) ,,y_(3)),(z_(1),,z_(2),,z_(3)):}| is equal to

Let overset(to)(a_(r))=x_(r )hat(i)+y_(r )hat(j)+z_(r )hat(k),r=1,2,3 three mutually prependicular unit vectors then the value of |{:(x_(1),,-x_(2),,x_(3)),(y_(1),,y_(2) ,,y_(3)),(z_(1),,z_(2),,z_(3)):}| is equal to

If vec a=x hat i+2 hat j-\ z hat k and vec b=3 hat i-\ y hat j+ hat k are two equal vectors, then write the value of x+y+zdot

If vec a=x hat i+2 hat j-z hat k\ and vec b=3 hat i-y hat j+ hat k are two equal vectors, then write the value of x+y+zdot

If vec r=x hat i+y hat j+z hat k ,\ then write the value of | vec rxx hat i|^2dot

If vec r=x hat i+y hat j+z hat k ,\ find the value of ( vec rxx hat i)dot (( vec rxx hat j))+x ydot

If the vectors hat(i) - 2x hat(j) + 3 y hat(k) and hat(i) +2x hat(j) - y hat(k) are perpendicular, then the locus of (x,y) is

Let vec a=a_1 hat i+a_2 hat j+a_2 hat k , vec b=b_1 hat i+a_2 hat j+b_2 hat k , and vec c=c_1 hat i+c_2 hat j+c_2 hat k , be three non-zero vectors such that vec c is a unit vector perpendicular to both vectors vec a and vec b . If the angle between a and b is pi//6, then |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]|^2 is equal to

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these