MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Condition for Coplanarity of Four Points

a⃗-2b⃗+3c⃗;2a...

Question

$\to a - 2 \to b + 3 \to c; 2 \to a + 3 \to b$ & $- 7 \to b + 10 \to c z$ Show that the points are notcolinear.

Open in App

Solution

$\begin{matrix} G i v e n, - - \to O A = ¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c - - \to O B = ¯ ¯¯¯¯ ¯ 2 a + 3 ¯ ¯ b - - \to O C = - 7 ¯ ¯ b + 10 ¯ ¯ c - - \to A B = - - \to O B - - - \to O A = (¯ ¯¯¯¯ ¯ 2 a + 3 ¯ ¯ b) - (¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c) = ¯ ¯ ¯ a + 5 ¯ ¯ b - 3 ¯ ¯ c - - \to A C = - - \to O C - - - \to O A = (- 7 ¯ ¯ b + 10 ¯ ¯ c) - (¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c) = - 5 ¯ ¯ b + 10 ¯ ¯ c - ¯ ¯ ¯ a + 2 ¯ ¯ b - 3 ¯ ¯ c = - ¯ ¯ ¯ a - 5 ¯ ¯ b + 7 ¯ ¯ c t h e r e e x i s t s n o . λ, s u c h t h a t - - \to A B = - - \to A C ∴ p o i n t s a r e n o t c o l l i n e a r \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the position vectors of three points are

\to a - 2 \to b + 3 \to c, 2 \to a + 3 \to b + 4 \to c, - 7 \to b + 10 \to c

, then the three points are

Q. The set of vectors

\to a - 2 \to b + 3 \to c

2 \to a + 3 \to b - 4 \to c

7 \to b - 10 \to c

are an example of co-planar vectors. Then the statement is true or false.

Q. The position vectors of

A, B, C, D

\to a, \to b, 2 \to a + 3 \to b

\to a - 2 \to b

respectively. Show that

- - \to D B = 3 \to b - \to a

- - \to A C = \to a + 3 \to b

Q. Four points given by position vectors

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

are coplanar, where

\to a, \to b a n d \to c

are non-coplanar vectors.

7 \to a - \to c

divides the join of points given by the position vectors

\to a + 2 \to b + 3 \to c

- 2 \to a + 3 \to b + 5 \to c

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Condition for Coplanarity of Four Points

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon