MyQuestionIcon

1

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

Section Formula

Let A and ...

Question

Let $A$ and $B$ be points with position vectors $¯ ¯ ¯ a$ and $¯ ¯ b$ with respect to origin $O$ . If the point $C$ on $O A$ is such that $2 ¯ ¯¯¯¯¯¯ ¯ A C = ¯ ¯¯¯¯¯¯ ¯ C O$ , $¯ ¯¯¯¯¯¯¯ ¯ C D$ is parallel to $¯ ¯¯¯¯¯¯ ¯ O B$ and $| ¯ ¯¯¯¯¯¯¯ ¯ C D | = 3 | ¯ ¯¯¯¯¯¯ ¯ O B |$ then $A D$ is

A

¯ ¯ b - \frac{a}{9}

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

B

3 ¯ ¯ b - \frac{a}{3}

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

C

¯ ¯ b - \frac{a}{3}

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

D

¯ ¯ b + \frac{a}{3}

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

Open in App

Solution

The correct option is B $3 ¯ ¯ b - \frac{a}{3}$
Given that $2 - - \to A C = - - \to C O$
$2 (\to c - \to a) = - \to c$
$3 \to c = 2 \to a$
$\to c = \frac{2 \to a}{3}$
Also given $- - \to C D | | - - \to O B$
$\Rightarrow \to a - \to c = k \to b$
$\Rightarrow ∣ ∣ \to d - \to c ∣ ∣ = 3 ∣ ∣ \to b ∣ ∣$
$\Rightarrow k ∣ ∣ \to b ∣ ∣ = 3 ∣ ∣ \to b ∣ ∣$
$\Rightarrow k = 3$
and $\to d = \to c + 3 \to b$
$\Rightarrow - - \to A D = \to d - \to a$ $= 3 \to b + \to c - \to a$
$\Rightarrow - - \to A D = 3 \to b - \frac{\to a}{3}$

Suggest Corrections

thumbs-up

1

Similar questions

O, A, B, C, D

O A = a, O B = b, O C = 2 a + 3 b

O D = a - 2 b .

| a | = 3 | b |,

then the angle between

B D

A C

O, A, B, C

are the vertices of a pyramid and

P, Q, R, S

are the mid-points of

O A, O B, B C, A C

respectively. If

- - \to O A = a, - - \to O B = b, - - \to O C = c,

express in terms of

a, b, c

- - \to O P, - - \to O Q, - - \to O R

- - \to O S

Q. The points O,A,B,C,D are such that

¯ ¯¯¯¯¯¯ ¯ O A = a, ¯ ¯¯¯¯¯¯ ¯ O B = b, ¯ ¯¯¯¯¯¯ ¯ O C = 2 a + 3 b

¯ ¯¯¯¯¯¯¯ ¯ O D = a - 2 b

| a | = 3 | b |

, then the angle between

¯ ¯¯¯¯¯¯¯ ¯ B D

¯ ¯¯¯¯¯¯ ¯ A C

\to a

\to b

be two unit vectors such that

| \to a + \to b | = \sqrt{3}

\to c = \to a + 2 \to b + 3 (\to a \times \to b),

2 | \to c |

Q. If A & B are point on the parabola

y^{2} = 4 a x

with vertex O such that OA perpendicular to OB & having lengths

r_{1}

r_{2}

respectively, then the value of

\frac{r_{1}^{4 / 3} r_{2}^{4 / 3}}{r_{1}^{2 / 3} + r_{2}^{2 / 3}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Law of Conservation of Energy

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Section Formula

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon