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 `0` b. `+-1` c. `+-2` d. none of these

If vec a_r=x_r hat i+y_r hat j+z_r hat k , where r=1,2,3 are three mutually perpendicular unit vectors, then possible values of the determinant |x_1x_2x_3y_1y_2y_3z_1z_2z_3|a r e

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=xhat i+2hat j-zhat k and vec b=3hat i-yhat j+hat k are two equal vectors,then write the value of x+y+z.

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

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

If x hat(i) + y hat(j) + z hat(k) is a unit vector and x:y:z= sqrt3:2:3 then what is the value of z?

If x hat(i)+ y hat(j)+zhat(k) is a unit vector and x:y:z=sqrt(3):2:3 , then what is the value of z?

Find the value of x and y if the vectors vec a=3hat i+xhat j-hat k and vec b=2hat i+hat j+yhat k are mutually perpendicular vectors of equal magnitude.

Find the values of x and y if the vectors vec a=3hat i+xhat j-hat k and vec b=2hat i+hat j+yhat k are mutually perpendicular vectors of equal magnitude.