A vector `oversetrarra` has components 2p and 1 with respect to a rectangular Cartesian system, this system is rotated through a certain clockwise sense, if we write the new system `oversetrarr a` has components (p+1) and 1 then

A vector has component A_1, A_2a n dA_3 in a right -handed rectangular Cartesian coordinate system O X Y Zdot The coordinate system is rotated about the x-axis through an angel pi//2 . Find the component of A in the new coordinate system in terms of A_1, A_2, a n dA_3dot

the mirror image of point (3,1,7) with respect to the plane x-y+z=3 is P . then equation plane which is passes through the point P and contains the line x/1=y/2=z/1 .

The axes of coordinates are rotated about the z-axis through an angle of pi//4 in the anticlockwise direction and the components of a vector are 2sqrt2, 3sqrt2, 4 . Prove that the components of the same vector in the original system are -1, 5, 4 .

This graph expresses the various steps of the system containing 1 mol of gas. Which type af process system has when it moves from C to A?

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q . Then (a) a^2+b^2=p^2+q^2 (b) 1/(a^2)+1/(b^2)=1/(p^2)+1/(q^2) (c) a^2+p^2=b^2+q^2 (d) 1/(a^2)+1/(p^2)=1/(b^2)+1/(q^2)

A variable line passes through a fixed point (x_(1),y_(1)) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes)

In a reversible process, if changes in entropy of the system and its surroundings are DeltaS_(1) & DeltaS_(2) respectively, then-

A circular coil of N turns is made of a conducting wire of a certain length . When a current I is sent through it , the magnetic moment is p , Another coil of 2N turns is made with the same wire and the same current is sent through it . The magnetic moment becomes p'. If p : p ' = n : 1 , what is the value of n ?