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- Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal point Q(-5, 2, 2).The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by the alpha angle and at the same time rotated in the positive xy direction by the beta angle, how is the new vector defined?Find terminal point Q of vector PQ = <9, −2, 1> with the initial point at P(−2, 4, 7)
- The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain, in general?)Find the component form and length of the vector v that has initial point (3, −7) and terminal point (−2, 5).2). Express the vector v with initial point P and terminal point Q in component form. P(-1, 4), Q(-7, -1) v=???
- If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector? What if the scalar is zero? Negative?Find the vectorequationof the line of intersection of the planes 2x-3y–z=5 and x+y+2z=1.Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.