In quadrilateral ABCD- AB-a- BC-b- AD-b-a- If M is the mid point of BC and N is a point on DM such that DN-45DM- then AN-

Let point A be taken as origin. Then the position vectors of B, C and D are a, a+b and b a respectively. P.V. of M=a+b+a2=a+b2 DN=45DM ⇒DN:NM=4:1 P.V. of N=4(a+ ...

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

Byju's Answer

Standard XII

Mathematics

Dot Product

In quadrilate...

Question

In quadrilateral $A B C D, - - \to A B = \to a, - - \to B C = \to b, - - \to A D = \to b - \to a .$ If $M$ is the mid point of $- - \to B C$ and $N$ is a point on $- - \to D M$ such that $- - \to D N = \frac{4}{5} - -- \to D M,$ then $- - \to A N =$

\frac{1}{5} - - \to A C

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

\frac{2}{5} - - \to A C

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

\frac{3}{5} - - \to A C

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

\frac{4}{5} - - \to A C

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

Open in App

Solution

The correct option is C $\frac{3}{5} - - \to A C$
Let point $A$ be taken as origin. Then the position vectors of $B, C$ and $D$ are $\to a, \to a + \to b$ and $\to b - \to a$ respectively.
P.V. of $M = \frac{\to a + \to b + \to a}{2} = \to a + \frac{\to b}{2}$
$- - \to D N = \frac{4}{5} - - \to D M$
$\Rightarrow - - \to D N : - -- \to N M = 4 : 1$
P.V. of $N = \frac{4 ⎛ ⎝ \to a + \frac{\to b}{2} ⎞ ⎠ + \to b - \to a}{5} = \frac{3}{5} (\to a + \to b)$
$\Rightarrow - - \to A N = \frac{3}{5} - - \to A C$

Suggest Corrections

Similar questions

\to A

and

\to B

represent force acting on a body in Newton.

\to A

has a magnitude of

3 N

. Then comment on the magnitude of

\to B

Q. For any three vectors

\to a, \to b

and

\to c

, prove that vectors

\to a - \to b, \to b - \to c

and

\to c - \to a

are coplanar.

Q. If

\to a

and

\to b

are two non zero vectors such that

\to a \times \to b = \to b \times \to a,

then

Q. If

[\to a \times \to b \to b \times \to c \to c \times \to a] = λ [\to a \to b \to c]^{2}

, then

λ

is equal to

Q. If

\to a =^i +^j +^k

, and

\to b =^j -^k

then area vector of plane formed by

\to a

and

\to b

Join BYJU'S Learning Program

Explore more

Dot Product

Standard XII Mathematics

Join BYJU'S Learning Program

In quadrilateral ABCD, −−→AB=→a, −−→BC=→b, −−→AD=→b−→a. If M is the mid point of −−→BC and N is a point on −−→DM such that −−→DN=45−−−→DM, then −−→AN=

In quadrilateral $A B C D, - - \to A B = \to a, - - \to B C = \to b, - - \to A D = \to b - \to a .$ If $M$ is the mid point of $- - \to B C$ and $N$ is a point on $- - \to D M$ such that $- - \to D N = \frac{4}{5} - -- \to D M,$ then $- - \to A N =$