Vectors dot and cross product help?

Question

1. A = (i) and B = (j). For A • B

a. What is its magnitude? (I think the answer is 0)

b. What its its direction? (I think the answer is none)

2. Show that i x j = -j x i

Is it just k = k?

3. Justify as to whether or not there can be a vector perpendicular to A x B. A = (3i + 2j) and B = (-3i - 2j).

4. For A = (-2i - 4j), B = (-i + j -k) and C= (4i + 2k). What is A • B • C? (I believe that answer is undefined?)

Answer 1

1. (A) = (i) = 1(i)

    (B) = (j) = 1(j)

hence, (A).(B) = 1x1 cos (pi/2) since angle between (i) and (j) is (pi/2)

                     = 0

dot product is a scalar quantity. no question of direction for A.B

2.  yeah

3. A X B = -6 (k) + 6(k) = 0 since (i) X(-i) = 0 (k), (i) X (-j) = 1(-k), (j) X (-i) = 1 (k), (j) X (-j) = 0 (k)

since A X B is a zero vector, no perpendicular vector exists.

4. do A.B, then do (A.B).C the answer will not be undefined. remember dot product of a zero vector is zero.

Answer 2

You are right in 1. & 2.

3. A X B = k [-6 - (-6)] = k(0) =0. No perpendicular vector

4. A = (-2i - 4j), B = (-i + j -k) and C= (4i + 2k).

A . B = 2 - 4 = - 2

A . B . C = - 2 C  {A . B gives a scalar multiplier to C}