Solve the followings: (1) If the position vectors of A,B,C are respectively -5i+j , 5i+5j and 10i+7j . Then show that A,B,C are collinear. (2) If vector a= 2i-5j+3k and vector b= i-2j-4k ,then find the value of |3a(vector)+2b(vector)|

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Q. If A and B are two perpendicular vectors given by

¯ ¯¯ ¯ A = 5 ¯ i + 7 ¯ j + 3 ¯ ¯ ¯ k

, and

4 ¯ ¯¯ ¯ B = 2 ¯ i + 2 ¯ j + c ¯ ¯ ¯ k

, then the value of

c

is:

The position vectors of four [point A, B, C and D are $ˆ i + ˆ j + ˆ k, 2 ˆ i + 5 ˆ j, 3 ˆ i + 2 ˆ j - 3 ˆ k, ˆ i - 6 ˆ j - ˆ k$ then select the correct relation:

Q. Show the each of the following triads of vectors are coplanar:
(i)

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

(ii)

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

(iii)

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

Q. If

4 ˆ i + 7 ˆ j + 8 ˆ k

2 ˆ i + 3 ˆ j + 4 ˆ k

and

2 ˆ i + 5 ˆ j + 7 ˆ k

are the position vectors of the vertices

A, B

, and

C

respectively of triangle

A B C

, then the position vector of the point where the bisector of angle

A

meets

B C

Q. The plane which can be formed with the vectors

¯ ¯ ¯ a = 3 ¯ i - 4 ¯ j + 2 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i - ¯ j - 6 ¯ ¯ ¯ k

¯ ¯ c = 5 ¯ i - 5 ¯ j - 4 ¯ ¯ ¯ k

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