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Homework Statement
Determin if the plan given by (-x+2z=10) and the line given by r=<5,2-t,10+4t> are othogonal,parllel or neither??
What is the solution?
The answer is that it depends on the values of x and z in the given equation. If x and z are both equal to 0, then Pln and Line are parallel. If x and z are not equal to 0, then Pln and Line are neither parallel nor orthogonal.
To determine if two lines are orthogonal, you can use the dot product formula. If the dot product of the two lines is equal to 0, then the lines are orthogonal. To determine if two lines are parallel, you can compare the slopes of the two lines. If the slopes are equal, then the lines are parallel.
No, Pln and Line cannot be both orthogonal and parallel. If two lines are orthogonal, they intersect at a 90 degree angle. If two lines are parallel, they never intersect. Therefore, they cannot be both orthogonal and parallel.
To find the equation of a line that is parallel to Pln, you can use the slope-intercept form of a line (y=mx+b) and substitute the slope of Pln for m. Then, you can plug in the coordinates of the given point for x and y to solve for b. This will give you the equation of the parallel line.
Yes, you can use a graph to determine if two lines are orthogonal or parallel. If the lines are orthogonal, they will intersect at a 90 degree angle. If the lines are parallel, they will never intersect and will have the same slope. You can also use a protractor to measure the angle between the lines to determine if they are orthogonal.