Given AB = -i + 3j and AC = 4i - 5j. Find BC. Also, if the positional vector of point A is u and the positional vector of point B is v, find vector AB in terms of u and v.

Here are the solutions to Questions 4 and 5. Question 4: Given AB = -i + 3j and AC = 4i - 5j. Find BC. Step 1: Express BC in terms of the given vectors. We can use the triangle law of vector addition. To go from B to C, we can go from B to A, and then from A to C. BC = BA + AC Step 2: Find BA from AB. The vector BA is the negative of AB. BA = -AB = -(-i + 3j) = i - 3j Step 3: Substitute the vectors into the expression for BC and calculate. BC = (i - 3j) + (4i - 5j) BC = (1+4)i + (-3-5)j BC = 5i - 8j The vector BC is: 5i - 8j Question 5: The positional vector of point A is u and the positional vector of point B is v. Find vector AB in terms of u and v. Step 1: Understand positional vectors. The positional vector of point A, u, means OA = u. The positional vector of point B, v, means OB = v. Step 2: Express AB using positional vectors. To find the vector from point A to point B, we subtract the positional vector of the starting point (A) from the positional vector of the ending point (B). AB = OB - OA Step 3: Substitute the given positional vectors. AB = v - u The vector AB in terms of u and v is: v - u Last free one today — make it count tomorrow, or type /upgrade for unlimited.