Question 8 of 68intermediate🔧 ApplyShort Answer2 marks

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (-5, 7).

Correct Answer

Scalar components: -7 and 6 Vector components: −7i^-7\hat{i} and 6j^6\hat{j}

Exercise: EXERCISE 10.2 | Q: 5 | (Page 17)
For More Understanding

Explanation

This question is from Exercise 10.2, Question 5. The question asks to find both scalar and vector components of a vector given its initial and terminal points. Following Example 10 in the context, when finding a vector joining two points P (initial) and Q (terminal), we subtract the coordinates of the initial point from the terminal point coordinates. The scalar components are the numerical coefficients of the unit vectors, while the vector components are the individual terms with their respective unit vectors.

Solution Steps

  1. Step 1: Let the initial point be A(2, 1) and terminal point be B(-5, 7).

  2. Step 2: The vector joining A and B is given by: AB→=(−5−2)i^+(7−1)j^\overrightarrow{AB} = (-5 - 2)\hat{i} + (7 - 1)\hat{j}

  3. Step 3: Simplifying: AB→=−7i^+6j^\overrightarrow{AB} = -7\hat{i} + 6\hat{j}

  4. Step 4: Scalar components are the coefficients: -7 and 6

  5. Step 5: Vector components are: −7i^-7\hat{i} and 6j^6\hat{j}

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