Given AB = −i + 3j and AC = 4i − 5j. Find BC. Also, if the positional vector of point A is u and the…

Question

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.

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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

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.

Answers

Step-by-step solution

Part 4· 3 steps

Express $\vec{BC}$ in terms of the given vectors.

Find $\vec{BA}$ from $\vec{AB}$ .

Substitute the vectors into the expression for $\vec{BC}$ and calculate.

Part 5· 3 stepsv - u

Understand positional vectors.

Express $\vec{AB}$ using positional vectors.

Substitute the given positional vectors.

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