Question

i and j are unit vectors along x and y axis respectively. What is the magnitude and direction of the vectors i + j, and i − j ? What are the components of a vector A= 2i + 3j along the directions of i + j and i − j? [You may use graphical method]

Answer 1

Answer on Question #58241, Physics / Mechanics | Relativity

i and j are unit vectors along x and y axis respectively. What is the magnitude and direction of the vectors i + j, and i - j? What are the components of a vector A = 2i + 3j along the directions of i + j and i - j? [You may use graphical method]

Solution:

$\vec{i}(1;0)$

$\vec{j}(0;1)$

$\vec{i} + \vec{j}(1; 1)$

$$| \vec {i} + \vec {j} | = \sqrt {1 ^ {2} + 1 ^ {2}} = \sqrt {2}$$$$\begin{array}{l} \vec{i}(1; 0) \\ \vec{j}(0; -1) \\ \vec{i} - \vec{j}(1; -1) \\ |\vec{i} - \vec{j}| = \sqrt{1^2 + (-1)^2} = \sqrt{2} \end{array}$$

The components of a vector $A = 2i + 3j$ along the directions of $\vec{i} + \vec{j} \colon \vec{A}(2; 3)$.

The components of a vector $A = 2i + 3j$ along the directions of $\vec{i} - \vec{j} \colon \vec{A}(2; -3)$.

**Answer:**

$$|\vec{i} + \vec{j}| = \sqrt{2}$$ $$|\vec{i} - \vec{j}| = \sqrt{2}$$ $$\vec{A}(2; 3)$$ $$\vec{A}(2; -3).$$

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