Find the values of x and y so that the vectors 2î + 3ĵ and xî + yĵ…

Question 7 of 68beginner🔧 ApplyNumerical1 mark

Find the values of x and y so that the vectors 2î + 3ĵ and xî + yĵ are equal.

Correct Answer

Since two vectors are equal if and only if their corresponding components are equal, we compare the coefficients of $\hat{i}$ and $\hat{j}$ in the given vectors $2\hat{i} + 3\hat{j}$ and $x\hat{i} + y\hat{j}$ .

Comparing the coefficients, we get: Coefficient of $\hat{i}$ : $x = 2$ Coefficient of $\hat{j}$ : $y = 3$

Thus, the values are $x = 2$ and $y = 3$ .

Exercise: EXERCISE 10.2 | Q: 4 | (Page 17)

For More Understanding

Explanation

The solution relies on the fundamental property of vector equality provided in the context, which states that 'the vectors $\vec{a}$ and $\vec{b}$ are equal if and only if $a_1 = b_1, a_2 = b_2 \text{ and } a_3 = b_3$ '. By applying this rule to the two-dimensional vectors given in the question, we equate the scalar components of $\hat{i}$ and $\hat{j}$ separately to find the values of the unknown variables.

Solution Steps

Step 1: Identify the corresponding components of the vectors $2\hat{i} + 3\hat{j}$ and $x\hat{i} + y\hat{j}$ .
Step 2: Equate the coefficients of $\hat{i}$ to find $x$ . We have $x = 2$ .
Step 3: Equate the coefficients of $\hat{j}$ to find $y$ . We have $y = 3$ .

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