Chapter 1.3, Problem 1AEXP

Find the cross product à x b and verify that it is orthogonal to both å and b for å =i+ 3j – 2k and b = -ỉ + 5k.

(b) If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

I do not know how to find t. Please help me.

Use the right-hand rule and the properties of the cross product to make the following calculations. (a) ((5 + k) x j) x k = (b) (ĩ+3) × (i × J) = (c) 4k x (k +j) = (d) (i +j) × (i – 3) =

Use the geometric definition of the cross product and the properties of the cross product to make the following calculations. (a) ((j + k) × j) × k = (b) (i+j) × (¹ × 3) = (c) 3k x (k+j) = (d) (i + j) × (i − 3) =

2. Find the V.A and H.A r(x) = 2+2x+3 x2-5x V.A- H.A-

Let Det (B)= 4 and Det (A) = x  y  zp  q  ra  b  c  = 3 . Then compute the following: A. Det(BAt )                                                      B. Det(A2B-1) C. 2x 2y 2z     p   q     r     a    b    cD. p  q  r     x  y  z     a  b  c