# Question Video: Finding the Horizontal Component of a Vector Shown on a Grid Physics

The vector π¨ can be written in the form π_(π₯)π’ + π_(π¦)π£. What is the value of π_(π₯), What is the value of π_(π¦)?

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### Video Transcript

The vector π¨ can be written in the form π sub π₯ π’ hat plus π sub π¦ π£ hat. What is the value of π sub π₯, and what is the value of π sub π¦?

Letβs first recall the meanings of π’ hat and π£ hat. These are unit vectors. And since our vector is drawn onto a grid, we can define one grid square to be one unit such that one unit in the horizontal direction is equal to π’ hat and one unit in the vertical direction is equal to π£ hat. So letβs first look at what is the value of π sub π₯. π sub π₯ is the number that we need to multiply by the unit vector π’ hat to make the horizontal component of the vector π¨.

So we start from the tail of vector π¨, and note that it touches the vertical axis. So we start from the vertical axis and count horizontally towards the tip of vector π¨ one, two units. But note that we went to the left from the axis, whereas the unit vector π’ hat increases to the right, which means that the number of units in the horizontal direction is negative two. So the answer to βWhat is the value of π sub π₯?β is negative two.

Next, letβs look at the value of π sub π¦. π sub π¦ is the number we need to multiply by the unit vector in the vertical direction π£ hat to get the vertical component of the vector π¨. So again, we start from the tail of vector π¨, and note that it touches the horizontal axis. So we start from the horizontal axis and count vertically towards the tip of vector π¨ one, two, three, four, five units. And note that we counted upwards from the axis, which is the same direction as the unit vector π£ hat. So the number of units in the vertical direction is positive five, which makes the answer to βWhat is the value of π sub π¦?β five.