Consider the vector v 1 3 a Find all values of k such that

Consider the vector v = (1, -3). a. Find all values of k such that u = (k, 6) is orthogonal to v b. Find all values of k such that u = (k, 6) is parallel to v

Solution

a. If u is orthogonal to v, then u.v = 0 i.e. ( k,6). (1,-3) = 0 or, k -18 = 0 so that k = 18.

b. Since 6 =( -2)*(-3) , hence the vector (k,6) will be parallel to the vector v = (1,-3) if k = (-2)(1) = -2.