CameraIcon

SearchIcon

MyQuestionIcon

8

You visited us 8 times! Enjoying our articles? Unlock Full Access!

Definition of Vector

The component...

Question

The component of a vector $\to a$ along and perpendicular to a nonzero vector $\to b$ is:

Open in App

Solution

$- - \to O A = \to a$ and $M$ is the foot of perpendicular on $O B$ .
The scalar component of $\to a$ along $\to b = O M$
$= ∣ ∣ \to a ∣ ∣ cos θ$
$= \to a . \frac{\to b}{∣ ∣ ∣ \to b ∣ ∣ ∣}$
The scalar component of $\to a$ perpendicular to $\to b = A M$
$= ∣ ∣ \to a ∣ ∣ sin θ$
$= \frac{∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}{∣ ∣ ∣ \to b ∣ ∣ ∣}$
The vector component of $\to a$ along $\to b = - - \to O M$
$= O M \frac{\to b}{∣ ∣ ∣ \to b ∣ ∣ ∣}$
$= \frac{(\to a . \to b) \to b}{\to b . \to b}$
The vector component of $\to a$ perpendicular to $\to b$
$\Rightarrow - - \to M A = - - \to O A - - - \to O M$
$= \to a - \frac{(\to a . \to b) \to b}{(\to b . \to b)}$
$= \frac{\to b \times (\to a \times \to b)}{\to b . \to b}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Can a vector have zero component along a line and still have nonzero magnitude?

Q. The components of a vector

\to a

along the perpendicular to the non-zero vector

\to b

are respectively

a, b

are nonzero vectors and

a

is perpendicular to

b

a

has nonzero vector

r

r \cdot a = α,

for some scalar

α, a \times r = b

Find component of vector $\to A$ along the direction of $\to B$ A||B and in perpendicular direction of $\to B$ $A ⊥ B$ .

Find component of vector $\to A$ along the direction of $\to B$ i.e. A||B and in perpendicular direction of $\to B$ that is $A_{⊥_{B}}$ .

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definition of Vector

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon