CameraIcon

SearchIcon

MyQuestionIcon

1

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

Addition of Vectors

Let G be th...

Question

Let $G$ be the centroid of a triangle $A B C$ . If $A B = a, A C = b$ then the bisector $A G$ , in terms of vectors $a$ and $b$ is

A

\frac{2}{3} (a + b)

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

B

\frac{1}{6} (a + b)

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

C

\frac{1}{3} (a + b)

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

D

\frac{1}{2} (a + b)

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

Open in App

Solution

The correct option is C $\frac{1}{3} (a + b)$
Take $A$ as origin.
Then position vectors of $A, B, C$ are given $0, a$ and $b$ respectively.
Then the centroid $G$ has position vector
$\frac{0 + a + b}{3} = \frac{a + b}{3}$
$∴ A G = \frac{a + b}{3}$

Suggest Corrections

thumbs-up

0

Similar questions

G

be the centroid of

△ A B C

- - \to A B = \to a

- - \to A C = \to b,

- - \to A G

\to a

\to b

Q. Let G be the centroid of ∆ ABC. If

\vec{A B} = \vec{a,} \vec{A C} = \vec{b,}

then the bisector

\vec{A G},

\vec{a} and \vec{b}

\frac{2}{3} (\vec{a} + \vec{b})

\frac{1}{6} (\vec{a} + \vec{b})

\frac{1}{3} (\vec{a} + \vec{b})

\frac{1}{2} (\vec{a} + \vec{b})

Q. If two vectors

\vec{a} and \vec{b}

|\vec{a}| = 2, |\vec{b}| = 1 and \vec{a} \cdot \vec{b} = 1,

then find the value of

(3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) .

\to a

\to b

be two vectors such that

∣ ∣ ∣ 2 \to a + 3 \to b ∣ ∣ ∣ = ∣ ∣ ∣ 3 \to a + \to b ∣ ∣ ∣

and the angle between

\to a

\to b

60^{\circ} .

\frac{1}{8} \to a

is a unit vector, then

∣ ∣ ∣ \to b ∣ ∣ ∣

Q. In the given figure PQ|| RS. If

∠ 1 = (2 a + b)^{\circ} a n d ∠ 6 = (3 a - b)^{\circ}

, then the measure of

∠ 2

in terms of b is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Vector Addition

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Addition of Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon