The position vectors of points A and B are -3 k- and 3 -3 -3 k- respectively- The equation of a plane is r 5 -2 -7 k-9-0- Thepoints A and B -A- are on the opposite side of the planeB- nothing can be saidC- lie on the planeD- are on the same side of the plane

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Equation of a Plane Passing through a Point and Perpendicular to a Given Vector

The position ...

Question

The position vectors of points A and B are $^i -^j + 3^k$ and $3^i + 3^j + 3^k$ respectively. The equation of a plane is $¯ r (5^i + 2^j - 7^k) + 9 = 0$ . The points A and B :

lie on the plane

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are on the same side of the plane

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are on the opposite side of the plane

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nothing can be said

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Solution

The correct option is C are on the opposite side of the plane
Equation of the plane is
P = 5x + 2y – 7z + 9 = 0, A = (1, –1, 3), B = (3, 3, 3)
P(A) = 5 – 2 – 21 + 9 < 0, P(B) = 15 + 6 – 21 + 9 > 0
$∴$ Points A and B are on the opposite sides of the plane

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Similar questions

Q. The position vectors of point

A

and

B

are

^i -^j + 3^k

and

3^i + 3^j + 3^k

respectively. The equation of a plane is

r . (5^i + 2^j - 7^k) + 9 = 0

. The point

A

and

B

Show that the points $^i -^j + 3^k$ and $3 (^i +^j +^k)$ are equidistant from the plane $\to r . (5^i + 2^j - 7^k) + 9 = 0$ and lies on opposite side of it.

Q. The position vectors of the points

A, B, C

are

2^i +^j -^k,

3^i - 2^j +^k

and

^i + 4^j - 3^k

, respectively. These points

Q. The position vectors of the points

A, B, C

and

D

are

3^i - 2^j -^k, 2^i + 3^j - 4^k, -^i +^j + 2^k

and

4^i + 5^j + λ^k

respectively. If the points

A, B, C

and

D

lie on a plane, find the value of

λ

Q. Equation of the plane passing through a point with position vector

^i +^j -^k

and

⊥

er to the planes

¯ ¯ ¯ r . (^i + 2^j + 3^k) = 7

¯ ¯ ¯ r . (2^i - 3^j + 4^k) = 0

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The position vectors of points A and B are ^i−^j+3^k and 3^i+3^j+3^k respectively. The equation of a plane is ¯r(5^i+2^j−7^k)+9=0. The points A and B :

The correct option is C are on the opposite side of the planeEquation of the plane is P = 5x + 2y – 7z + 9 = 0, A = (1, –1, 3), B = (3, 3, 3) P(A) = 5 – 2 – 21 + 9 < 0, P(B) = 15 + 6 – 21 + 9 > 0 ∴ Points A and B are on the opposite sides of the plane

The position vectors of points A and B are $^i -^j + 3^k$ and $3^i + 3^j + 3^k$ respectively. The equation of a plane is $¯ r (5^i + 2^j - 7^k) + 9 = 0$ . The points A and B :

The correct option is C are on the opposite side of the plane
Equation of the plane is
P = 5x + 2y – 7z + 9 = 0, A = (1, –1, 3), B = (3, 3, 3)
P(A) = 5 – 2 – 21 + 9 < 0, P(B) = 15 + 6 – 21 + 9 > 0
$∴$ Points A and B are on the opposite sides of the plane