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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
- a)21
- b)17
- c)12
- d)11
Correct answer is option 'D'. Can you explain this answer?
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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z ...
Relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other is a1a2 + b1b2 + c1c2 = 0.
1(3) + 2(4) + k(-1) = 0
k(-1) = -11
k = 11
1(3) + 2(4) + k(-1) = 0
k(-1) = -11
k = 11
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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z ...
Perpendicularity of planes:
Two planes are perpendicular to each other if the normal vectors of the planes are perpendicular. The normal vector of a plane in the form Ax + By + Cz + D = 0 is given by (A, B, C).
Finding the normal vectors:
1. For the plane x + 2y + kz + 2 = 0, the normal vector is (1, 2, k).
2. For the plane 3x + 4y - z + 2 = 0, the normal vector is (3, 4, -1).
Checking perpendicularity:
For the planes to be perpendicular, the dot product of their normal vectors should be zero.
(1, 2, k) dot (3, 4, -1) = 1*3 + 2*4 + k*(-1) = 0
3 + 8 - k = 0
11 - k = 0
k = 11
Therefore, the value of k for the given planes to be perpendicular to each other is 11.
Two planes are perpendicular to each other if the normal vectors of the planes are perpendicular. The normal vector of a plane in the form Ax + By + Cz + D = 0 is given by (A, B, C).
Finding the normal vectors:
1. For the plane x + 2y + kz + 2 = 0, the normal vector is (1, 2, k).
2. For the plane 3x + 4y - z + 2 = 0, the normal vector is (3, 4, -1).
Checking perpendicularity:
For the planes to be perpendicular, the dot product of their normal vectors should be zero.
(1, 2, k) dot (3, 4, -1) = 1*3 + 2*4 + k*(-1) = 0
3 + 8 - k = 0
11 - k = 0
k = 11
Therefore, the value of k for the given planes to be perpendicular to each other is 11.
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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.a)21b)17c)12d)11Correct answer is option 'D'. Can you explain this answer?
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