WEBVTT
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in the question they're asking to determine whether the planes
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are parallel, perpendicular or neither. If neither then
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find the angle between them. The two equations of
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the planes are number one express two by minus that
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equal to two and number 22 x minus two.
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Y pass that equal to one. The first condition
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of taking whether these planes are parallel or not.
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We have to compare the coefficients, The coordinates of
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these two planes for the X, Y and Z
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coordinates respectively. That is one way to equal to
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two by minus two equal to minus one by one
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. That is, it will do half. That
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is not equal to-1 and not equal to minus
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one as all three three shoes are not equal.
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Mhm. So Mhm. These planes are not Caroline
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. 2nd part is checking. These planes are perpendicular
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are not. What is it? So for this
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we have to find the normal vectors of these two
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planes. So normal victor, one is equal to
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1,-1. and the normal Vector two for
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the second plane is equal to 2-2. 1
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. Therefore we have to find the dot product of
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these two. Normal vectors, if it is equal
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to zero then these planes are perpendicular. Otherwise not
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therefore, and one vector. And to vector is
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equal to two minus 4-1, that is equal
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to-3 and this is not equal to zero.
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Therefore these planes are not what particular to each other
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. And the third point is if they are neither
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of this, if neither, then we have to
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find them anger between from these planes. Yeah.
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So in order to find the angle between these planes
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the formula is cost Theta is equal to the skill
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er one today of and two victor dot in one
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victor who divided by skill er off in to victor
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Multiplied by a scalar of in one victor. Therefore
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cost 3 to is equal to putting the values of
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the normal victims. And these killers we get The
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numerator to be to-4-1 divided by route under
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one squared plus two squared plus one square into he
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wrote under two square place to square place one square
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it won't. So casita is equal to-3 divided
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by Route Under six. In 2 route under nine
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this is equal to minus three divided by route under
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six. Multiplied by three and three and 3 from
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new murder and no Minuto gets canceled. So cost
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three to Is equal to-1 by Route six.
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So therefore tita Is equal to cause inverse of-1
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. by Route six. This value of Theta is
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equal to 114.07°. So in the question they have access
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to round The decimal digit up to one digit.
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So this is equal to 114.1 degree. Yeah And
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this is the angle between the two planes which is
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really quite answer of the given question. Just one