Represent the vector A → = 2 i ^ + 4 j ^ + 5 k ^ in matrix form.

Given A → = 2 i ^ + 4 j ^ + 5 k ^ We know that, A vector A → = a 1 i ^ + a 2 j ^ + a 3 k ^ can be visualised as either row or column matrix as a 1 a 2 a 3 or a 1 a 2 a 3 respectively. Therefore, the given vector can be represented in the matrix form as 2 4 5 or 2 4 5 .

Represent the vector A → = 2 i ^ + 4 j ^ + 5 k ^ in matrix form.

Given A → = 2 i ^ + 4 j ^ + 5 k ^ We know that, A vector A → = a 1 i ^ + a 2 j ^ + a 3 k ^ can be visualised as either row or column matrix as a 1 a 2 a 3 or a 1 a 2 a 3 respectively. Therefore, the given vector can be represented in the matrix form as 2 4 5 or 2 4 5 .

r → = s i ^ - t k ^ is the equation of :

a straight line joining the points i → and k →

r → = s i ^ + t j ^ is the equation of

a straight line joining the points i ^ and j ^

The position vector of the point of intersection of three planes r → · n → 1 = q 1 , r → · n → 2 = q 2 , r → · n → 3 = q 3 where n → 1 , n → 2 and n → 3 are non-coplanar vectors, is

r → = 1 n → 1 n → 2 n → 3 q 3 n → 1 × n → 2 + q 1 n → 2 × n → 3 + q 2 n → 3 × n → 1

r → = 1 n → 1 n → 2 n → 3 q 1 n → 1 × n → 2 + q 2 n → 2 × n → 3 + q 3 n → 3 × n → 1

r → = 1 n → 3 n → 1 n → 2 q 1 n → 1 × n → 2 + q 2 n → 2 × n → 3 + q 3 n → 3 × n → 1

EASY

Earn 100

Represent the vector $\vec{A} = 2 \hat{i} + 4 \hat{j} + 5 \hat{k}$ in matrix form.

Important Questions on Vector Algebra

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

\vec{r} = s \hat{i} - t \hat{k}

is the equation of :

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

\vec{r} = s \hat{i} + t \hat{j}

is the equation of

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

Let a vector

α \hat{i} + β \hat{j}

be obtained by rotating the vector

\sqrt{3} \hat{i} + \hat{j}

by an angle

45 °

about the origin in counterclockwise direction in the first quadrant. Then the area (in sq. units) of triangle having vertices

(α, β), (0, β)

and

(0, 0)

is equal to

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

The vector

2 \hat{j} - \hat{k}

lies

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

Vector

\vec{P} = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}

makes angle from

Z

-axis equal to

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

Let

\vec{a} = \hat{i}

be a vector which makes an angle of

120 °

with a unit vector $\vec{b}$ . Then, the unit vector

(\vec{a} + \vec{b})

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

A bird flies at an angle of

60^{o}

to the horizontal. Its horizontal component of velocity is

10 {m s}^{- 1} .

Find the vertical component of velocity in

{m s}^{- 1} .

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

Let

A

be a point in space such that

| OA | = 12,

where

O

is the origin. If

O A

is inclined at angles

45 °

and

60 °

with

X

-axis and

Y

-axis respectively, then what is

O A

equal to?

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

A girl walks 4 km westward. then she walks 3 km in a direction 30^o East of North and stop. Then, the girl displacement from her initial point of departure, is

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

The position vector of the point of intersection of three planes

\vec{r} \cdot {\vec{n}}_{1} = q_{1}, \vec{r} \cdot {\vec{n}}_{2} = q_{2}, \vec{r} \cdot {\vec{n}}_{3} = q_{3}

where

{\vec{n}}_{1}, {\vec{n}}_{2}

and

{\vec{n}}_{3}

are non-coplanar vectors, is

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

What are the value of the angles which a vector

\hat{i} + \hat{j} + \sqrt{2} \hat{k}

makes with

X, Y

and

Z

axes respectively ?

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

\vec{a} = 4 \hat{i} + 6 \hat{j}

and

\vec{b} = 3 \hat{j} + 4 \hat{k},

, then the vector form of component of

\vec{a}

along

\vec{b}

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

A ladder is resting with the wall at an angle of

30 ° .

A man is ascending the ladder at the rate of

3 ft s^{- 1}

. His rate of approaching the wall is

HARD

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

A unit vector $a$ is making angle $\frac{π}{3}$ with $\hat{i}, \frac{π}{4}$ with $\hat{j}$ and an acute angle $θ$ with $\hat{k}$ .

$I$ . The value of $θ$ is $\frac{π}{3}$ .

$II$ . The components of $a$ are $\frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$ .

Which of the above statement(s) is/are correct?

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

If projection of any line on coordinate axes

3, 4

and

5

, then its length is

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

The magnitude of resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of the sides of an equilateral triangle taken in order is

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

What is the vertical component of a

5 N

force acting on a particle along a direction making an angle of

60 °

with vertical?

MEDIUM

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

A vector

\vec{a}

has components

2 p

and

1

with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system,

\vec{a}

has components

p + 1

and

1

, then

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

Given three vectors

\vec{a} = 6 \hat{i} - 3 \hat{j}

\vec{b} = 2 \hat{i} - 6 \hat{j}

and

\vec{c} = - 2 \hat{i} + 21 \hat{j}

such that

\vec{α} = \vec{a} + \vec{b} + \vec{c}

. Then, the resolution of the vector

\vec{α}

into components with respect to

\vec{a}

and

\vec{b}

is given by

EASY

Mathematics>Three Dimensional Geometry>Vector Algebra>Resolution of Vectors

In the figure which of the ways indicated for combining the $x$ and $y$ components of the vector $\vec{a}$ are proper to determine that vector?

Question Image

Represent the vector A→=2i^+4j^+5k^ in matrix form.

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

Represent the vector $\vec{A} = 2 \hat{i} + 4 \hat{j} + 5 \hat{k}$ in matrix form.