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Applications of Dot Product

Let a =3 î+ĵ+...

Question

Let $\to a = 3^i +^j + 2^k, \to b =^i - 2^j - 4^k$ be the position vectors of the point A and B, then the distance of the point $-^i +^j +^k$ from the plane passing through B and perpendicular to AB is ___

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Solution

Equation of the plane is 2x +3y + 6z + 28 = 0
Required answer is 5

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Similar questions

\to α = 3^i +^j + 2^k

\to β =^i - 2^j - 4^k

are the position vectors of the points

A

B .

Then the distance of the point

-^i +^j +^k

from the plane passing through

B

and perpendicular to

A B

\to α = 3^i +^j + 2^k

\to β =^i - 2^j - 4^k

are the position vectors of the points

A

B .

Then the distance of the point

-^i +^j +^k

from the plane passing through

B

and perpendicular to

A B

\to α = 3^i +^j + 2^k, \to β =^i - 2^j - 4^k

are the position vectors of the points

A

B

. Then the distance of the point

-^i +^j +^k

from the passing through

B

and perpendicular to

A B

\to α = 3^i +^j + 2^k

\to β =^i + 2^j - 4^k

are the position vectors of the points A and B. Then the distance of the point

-^i +^j +^k

from the plane passing through B and perpendicular to AB is

\frac{27}{\sqrt{k}}

.
Find sum of digits of k .

A, B, C

be points with position vectors

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

3^i +^j + 2^k

respectively. Find the shortest distance between point

B

O A C

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