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I see that you've uploaded an image containing problems from **Exercise 8.6** related to vectors. The questions involve various vector operations such as scalar multiplication, vector addition, and determining vector expressions.

Here's an outline of what I can assist with:

1. **Question 1**: Given that \( \overrightarrow{PQ} = (1, 9) \), you are tasked with finding \( \lambda \) when \( \overrightarrow{PQ} = \lambda \overrightarrow{PQ} \). There are four options for \( \lambda \) (4, -2, 1, and \(\frac{1}{3}\)).
   
2. **Question 2**: This problem involves finding the vector expression for \( 2a - 3b + c \), where \( a = 5i + 2j \), \( b = 3i - j \), and \( c = 4i - 7j \).

3. **Question 3**: This asks you to calculate the vector expressions for \( 5p + 2q \), where the position vectors of \( P \), \( Q \), and \( R \) are given as \( p = 5i - 4j \), \( q = -3i + 4j \), and \( r = 7i - j \).

4. **Question 4**: Involves finding vector expressions such as \( 2p - r \) and \( 3p + 2q \), where \( p = 2i \), \( q = i - j \), and \( r = 5j \).

5. **Question 5**: Given vectors \( OP = 3i + 9j \), \( OQ = 7i - 2j \), and \( OR = 4i + j \), you are tasked with finding certain combinations like \( \frac{1}{3}OP + 2OQ \) and others.

Would you like me to solve a particular question, or would you prefer a full solution of the exercise? Let me know how you'd like to proceed.

Vector operations involving position vectors and scalar multiples in problems from Exercise 8.6.

Explore how to solve vector operation problems involving position vectors and scalar multiplication from Exercise 8.6. This set covers vector addition, scalar multiplication, and position vector calculations. Suitable for high school students in Grades 10-12.

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