ABCD is a parallelogram. The position vector of the points A (4i+5j-10k) B (2i-3j+4k) C (-i+2j+k) Find vector eqn. Of the line BD. Also reduce it to cartesian form.

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Q. ABCD is a parallelogram. The position vectors of the points A, B and C are respectively,

4 \hat{i} + 5 \hat{j} - 10 \hat{k}, 2 \hat{i} - 3 \hat{j} + 4 \hat{k} and - \hat{i} + 2 \hat{j} + \hat{k} .

Find the vector equation of the line BD. Also, reduce it to cartesian form.

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

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

Q. If the points whose position vectors are

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

and

4 ¯ i + 5 ¯ j + λ ¯ ¯ ¯ k

are coplanar then show that

λ = \frac{- 146}{m}

.Find

m

Q. Constant forces

P = 2 i - 5 j + 6 k

and

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

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