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Properties of Determinants

A line passin...

Question

A line passing through the point A with position vector a= 4i+ 2j+2k is parallel to the vector b = 2i+3j+6k . Find the length of the perpendicular drawn on this line from a point P with position vector r= i + 2 j+ 3k

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Solution

The above answer is correct ,the way of solving is also correct. So there will be some errors in your text book please check it once more.

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Q. The distance of the point

B

with position vector

i + 2 j + 3 k

from the line passing through the point

A

with position vector

4 i + 2 j + 2 k

and parallel to the vector

2 i + 3 j + 6 k

Q. The distance of the point

B (i + 2 j + 3 k)

from the line which is passing through

A (4 i + 2 j + 2 k)

and which is parallel to the vector

c = 2 i + 3 j + 6 k,

Q. Constant forces

P = 2 i - 5 j + 6 k

Q = - i + 2 j - k

act on a particle is displaced from a point A with position vector

4 i - 3 j - 2 k

to point B with position vector

6 i + j - 3 k .

Calculate work done for this process is

Q. Find the vector equation of a line passing through the point with position vector

\hat{i} - 2 \hat{j} - 3 \hat{k}

and parallel to the line joining the points with position vectors

\hat{i} - \hat{j} + 4 \hat{k} and 2 \hat{i} + \hat{j} + 2 \hat{k} .

Also, find the cartesian equivalent of this equation.

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

2 \hat{i} - \hat{j} + \hat{k}

and perpendicular to the vector

4 \hat{i} + 2 \hat{j} - 3 \hat{k} .

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Properties of Determinants

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