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

Let and.Find ...

Question

Let and. Find a vector which is perpendicular to both and, and.

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Solution

Let.

Sinceis perpendicular to bothand, we have:

Also, it is given that:

On solving (i), (ii), and (iii), we get:

Hence, the required vector is.

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Q. Let and . Find a vector which is perpendicular to both and , and .

\vec{a} = \hat{i} + 4 \hat{j} + 2 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 7 \hat{k} and \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .

\vec{d}

which is perpendicular to both

\vec{a} and \vec{b}

and \vec{c} \cdot \vec{d} = 15 .

\vec{a} = 4 \hat{i} + 5 \hat{j} - \hat{k}, \vec{b} = \hat{i} - 4 \hat{j} + 5 \hat{k} and \vec{c} = 3 \hat{i} + \hat{j} - \hat{k}

. Find a vector

\vec{d}

which is perpendicular to both

\vec{c} and \vec{b} and \vec{d} . \vec{a} = 21

a = i - j, b = i + k

, find a unit vector c perpendicular to a and coplanar with a and b. also find a unit vector d perpendicular to both a and c.

\to a (3^i 22^j 22^k^b (^i 22^j 2^k .

Then a unit vector perpendicular to both

\to a \to b

\to a 2 \to b

Let $a =^i + 4^j + 2^k, b = 3^i - 2^j + 7^k$ and $c = 2^i -^j + 4^k$ . Find a vector d which is perpendicular to both a and b and c.d = 15

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