MyQuestionIcon

1

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

Position Vector

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c, \to d, \to e, \to f$ are position vectors of 6 points A, B, C, D, E & F respectively such that $3 \to a + 4 \to b = 6 \to c + \to d = 4 \to e + 3 \to f = \to x$ then

A

¯ ¯¯¯¯¯¯ ¯ A B

is parallel to

¯ ¯¯¯¯¯¯¯ ¯ C D

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

line AB, CD and EF are concurrent

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

\frac{\to x}{7}

is position vector of the point dividing CD in ratio 1 : 6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

A, B, C, D, E & F are coplanar

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
B line AB, CD and EF are concurrent
C $\frac{\to x}{7}$ is position vector of the point dividing CD in ratio 1 : 6
Given condition
$3 \to a + 4 \to b = 6 \to c + \to d = 4 \to e + 3 \to f = \to x$
It is clearly seen that sum of coefficient
$7 = 7 = 7 = \to x$
So lines are concurrent
position vector of c and d
$p o s i t i o n v e c t o r = \frac{6 c + d}{7}$
from above condition
$p o s i t i o n v e c t o r = \frac{x}{7}$

Suggest Corrections

thumbs-up

0

Similar questions

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

are the position vectors of the points

A, B, C, D

respectively such that

3 \to a + 5 \to b - 3 \to c - 5 \to d = 0

A B

C D

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.

A, B, C

D

are four points in a plane with Position Vectors

\to a, \to b, \to c

\to d

respectively such that

(\to a - \to d) . (\to b - \to c) = (\to b - \to d) . (\to c - \to a) = 0,

then for the triangle

A B C, D

A, B, C

D

have position vectors

\to a, \to b, \to c

\to d

, respectively, such that

\to a - \to b = 2 (\to d - \to c)

\to b, \to c, \to d

are non-coplanar vectors, then the vector

(\to a \times \to b) \times (\to c \times \to d) + (\to a \times \to c) \times (\to d \times \to b) + (\to a \times \to d) \times (\to b \times \to c)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Distance and Displacement

PHYSICS

Watch in App

explore_more_icon

Explore more

Position Vector

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon