How Do You Find the Line of Intersection Between Two Planes?

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In summary, a vector is a mathematical object with both magnitude and direction, represented by an arrow. To add or subtract vectors, place them head to tail and add/subtract corresponding components. A scalar only has magnitude, while a vector has both magnitude and direction. To find the magnitude and direction of a vector, use the Pythagorean theorem and trigonometry, respectively. It is not possible to multiply two vectors, but they can be scaled by a scalar.
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Scharles
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Given :
plane 1 : z=x+y
plane 2 : 2x-5y-2z=1

Find the equation of intersection of plane 1 and plane 2.

i have no idea how to solve 3 unknowns in 2 quations, please help~ thanks~
 
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  • #2
Simply substitute z=x+y to equation of plane 2 and you ll have an equation involving only x and y to the first order, so it will be the equation of a streight line.
 

FAQ: How Do You Find the Line of Intersection Between Two Planes?

1. What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is commonly represented by an arrow pointing in a specific direction, with the length of the arrow representing its magnitude.

2. How do I add or subtract vectors?

To add or subtract vectors, you must first place them head to tail. Then, you can add or subtract the corresponding components (x and y values) of each vector to get the resultant vector.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, such as speed or temperature. A vector has both magnitude and direction, such as velocity or force.

4. How do I find the magnitude and direction of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem (magnitude = √(x² + y²)). To find the direction, you can use trigonometry (direction = tan⁻¹(y/x)).

5. Can I multiply two vectors together?

No, it is not possible to multiply two vectors together. However, you can scale a vector by a scalar (a number) to change its magnitude.

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