Question Video: Finding the Horizontal Component of a Vector Shown on a Grid | Nagwa Question Video: Finding the Horizontal Component of a Vector Shown on a Grid | Nagwa

Question Video: Finding the Horizontal Component of a Vector Shown on a Grid Physics • First Year of Secondary School

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

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Video Transcript

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

Letβs first define π’ hat and π£ hat. These are unit vectors. So if we define one square in our graph to be one unit, then π’ hat is one square in the horizontal direction and π£ hat is one square in the vertical direction. π subscript π₯ is then the number we multiply by the unit vector to make the horizontal component of the vector π¨.

The tail of vector π¨ is on the vertical axis. So we just need to count the distance from the axis to the tip of vector π¨ to get the horizontal component. So starting from the axis, thatβs one, two, three, four, five. And note that when we go from the tail to the tip of π¨, weβre counting to the left in the horizontal direction, whereas the unit vector π’ went upwards to the right, which makes it negative five. So the answer to βWhat is the value of π subscript π₯?β is negative five.

Next, we need to find the value of π subscript π¦. So weβre doing the same thing in the vertical direction. The tail of vector π¨ is on the horizontal axis. So starting from the axis towards the tip of vector π¨, we have one, two, three, four. And that was in the downwards direction, whereas the unit vector π£ hat counts upwards, making this negative four. So the answer to βWhat is the value of π subscript π¦?β is negative four.

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