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`

A vector a has components a_1,a_2,a_3 in a right handed rectangular cartesian coordinate system OXYZ the coordinate axis is rotated about z axis through an angle pi/2 . The components of a in the new system

A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel alpha about the origin the anticlockwise sense. Statement 1: IF the vector has component p+2 and 1 with respect to the new system, then p=-1. Statement 2: Magnitude of the original vector and new vector remains the same.

The vector vec a has the components 2p and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel about the origin in the counterclockwise sense. If, with respect to a new system, vec a has components (p+1)a n d1 , then p is equal to a. -4 b. -1//3 c. 1 d. 2

Each question has four choices a, b, c, and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. a. Both the statements are TRUE and statement 2 is the correct explanation for Statement 1. b. Both the statements are TRUE but Statement 2 is NOT the correct explanation for Statement 1. c. Statement 1 is TRUE and Statement 2 is FALSE. d. Statement 1 is FALSE and Statement 2 is TRUE. A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel alpha about the origin the anticlockwise sense. Statement 1: IF the vector has component p+2 and 1 with respect to the new system, then p=-1. Statement 2: Magnitude of the origin vector and the new vector remains the same.

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

Show that all chords of the curve 3x^2-y^2-2x+4y=0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

Find the coordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x+y+z=7.

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

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