WEBVTT
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they're asking to find the parametric equations for the lines
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of intersection of the plains and also to find the
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angle between these planes. The equations of the planes
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are number one express wipers that equal to one and
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number two express to wipers to that equal to one
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. Now for questions A we have to find The
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parametric equations for the line of intersection of these two
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planes. So first we have to find the normal
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vectors of these two planes. So normal vector and
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one for the plain one is equal to the coefficients
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of each other coordinates of this plane, that is
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equal to 111, and similarly the Normal vector of
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the second plane is equal to 1- two.
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And in order to find the no these two vectors
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cross product. The values of n. one is
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1, 1, 1 And the values of into
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is 1- two. Therefore, after calculating the
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cross product, pick it. Value of the normal
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vector is equal to the values 0-1, 1
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. So in order to find a parametric equation of
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the lines of intersection of these two plane, we
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have to find a coordinate point of these two planes
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point of intersection. So the coordinate point of the
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line of intersection of these two planes can be evaluated
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as Yes. Okay, If you put the value
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of zero who said then the first equation takes the
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form Explains why equal to one. And the second
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equation takes the form Explains too why equal to one
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. Therefore by solving these two equations subtracting these two
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equations, X and one gets canceled. And therefore
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value of Why is equal to zero. So if
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we put this value of Y in the equation one
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we get the value of excess equal to one.
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Therefore we got the coordinate point for the line of
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intersection that is 100. Therefore in order to find
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out equation parametric equation. Oh the of these planes
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? Yeah that's right. Yeah bigot the equation as
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Yeah one into T into k cab. So after
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finding this equation we can write it equal to icap
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one into I cab-T into Jacob Plus T.
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in two K Cup. And in order to find
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though parliamentary equation we put the coefficient value of each
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of the direction vectors as X, Y and Z
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. Therefore the parametric equation. Off line of intersection
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. Yeah. Of these planes are X equal to
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one Why equal to minus T. And that equal
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to see. So this is the answer of the
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question. A in the given question. And next
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in the question they're asking to find the angle between
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these two plains. Mhm. So in question be
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they're asking to find the angle between these planes.
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Mhm. So in order to find the anger where
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to find cost heater. That is equal to the
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scalar value off and one vector dot and to victor
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who divided by and one vectors killer into into victor's
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killer. Mhm. Mhm. This is equal to
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one plus two plus two. All divided by route
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under one scripless Once privilege, one square hole into
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Route Under one sq Place to Square Place to Square
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. This is equal to five By three row 3
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. Therefore, in order to find the angle,
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pita is equal to cause inverse of five x 3
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. Route three to find out diluted in degrees.
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The corresponding value to this angle is equal to 15.803°
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and so. Mhm. Mhm. Yes, the
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value of the degree Rounded up to one decimal place
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is equal to 15.8°. So the answer to question number
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B is 15 point a degree. This is the
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angle between the two planes in the given question.