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Let $A B C$ be a triangle, the position vectors of whose vertices are respectively $7 \hat{\dot{j}} + 10 \hat{k}, - \hat{\dot{i}} + 6 \hat{\dot{j}} + 6 \hat{k}$ and $- 4 \hat{\dot{i}} + 9 \hat{\dot{j}} + 6 \hat{k}$ . Then, the $∆ A B C$ is

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Important Questions on Vector Algebra

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

The position vector of $A$ and $B$ are $2 \hat{i} + 2 \hat{j} + \hat{k}$ and $2 \hat{i} + 4 \hat{j} + 4 \hat{k}$ . The length of the internal bisector of $∠ B O A$ of triangle $A O B$ is

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

If the vectors

x \hat{i} - 3 \hat{j} + 7 \hat{k}

and

\hat{i} + y \hat{j} - z \hat{k}

are collinear then the value of

\frac{x y^{2}}{z}

is equal

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

The values of

α

such that

| α \hat{i} + (α + 1) \hat{j} + 2 \hat{k} | = 3

, are

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

Number of unit vectors of the form

a \hat{i} + b \hat{j} + c \hat{k},

where

a, b, c \in W

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

D, E

and

F

are respectively mid-points of

A B, A C

and

B C

∆ A B C

, then

\vec{B E} + \vec{A F}

is equal to

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

P Q R S T

is a pentagon, then the resultant of forces

\vec{P Q}, \vec{P T}, \vec{Q R}, \vec{S R}, \vec{T S}

and

\vec{P S}

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

The direction cosines of the vector

\hat{i} - 5 \hat{j} + 8 \hat{k}

are

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

A vector

\vec{a}

has components

3 p

and

1

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

\vec{a}

has components

p + 1

and

\sqrt{10},

then a value of

p

is equal to:

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

Find the component of vector

\vec{P} = 2 \hat{i} + 3 \hat{j}

along the direction of vector

\vec{Q} = \hat{i} + \hat{j} .

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

A unit vector is represented as

(0 .8 \hat{i} + b \hat{j} + 0 .4 \hat{k})

. Hence the value of

b

must be

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

The vector that is parallel to the vector

2 \hat{i} - 2 \hat{j} - 4 \hat{k}

and coplanar with the vectors

\hat{i} + \hat{j}

and

\hat{j} + \hat{k}

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

Let

\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + 2 \hat{j} + \hat{k}

and

\vec{c} = 5 \hat{i} + \hat{j} - \hat{k}

be three vectors. The area of the region formed by the set of points whose position vectors

\vec{r}

satisfy the equations

\vec{r} \cdot \vec{a} = 5

and

| \vec{r} - \vec{b} | + | \vec{r} - \vec{c} | = 4

is closest to the integer.

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

\vec{a} = \hat{i} + λ \hat{j} + 2 \hat{k} & \vec{b} = μ \hat{i} + \hat{j} - \hat{k}

are orthogonal and

|\vec{a}| = |\vec{b}|

, then

(λ, μ) =

HARD

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

In a triangle

A B C

, let

G

denote its centroid and let

M, N

be points in the interiors of the segments

A B, A C

, respectively, such that

M, G, N,

are collinear. If

r

denotes the ratio of the area of triangle

A M N

to the area of

A B C

then

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

If vectors

\vec{a_{1}} = x \hat{i} - \hat{j} + \hat{k}

and

\vec{a_{2}} = \hat{i} + y \hat{j} + z \hat{k}

are collinear, then a possible unit vector parallel to the vector

x \hat{i} + y \hat{j} + z \hat{k}

is:

HARD

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

What is the vector

r

of magnitude

2 \sqrt{3}

units that makes an angle of

\frac{π}{2}

and $\frac{\pi}{6}$ with

y

-axis and

z

-axis respectively?

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

If a vector

\vec{x}

makes angles with measure

\frac{π}{4}

and

\frac{5 π}{4}

with positive directions of

X

-axis and

Y

-axis respectively, then

\vec{x}

made angle of measure …... with positive direction of

Z

-axis

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

\vec{a}

is a nonzero vector of magnitude

‘ a ’

and

λ

a nonzero scalar then

λ \vec{a}

is unit vector if

MEDIUM

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

A person goes

2 km

east, then

3 km

north, then

4 km

west and then

1 km

north, starting from the origin. This point is taken as vector

A

The vector

B

B such that

3 A + 5 B = (9, 32),

EASY

Mathematics>Vectors and 3D Geometry>Vector Algebra>Basics of Vectors

\vec{A B} = 3 \hat{ı} + 5 \hat{j} + 4 \hat{k}

\vec{A C} = 5 \hat{i} - 5 \hat{j} + 2 \hat{k}

represent the sides of a triangle

A B C

, then the length of the median through

A

Let ABC be a triangle, the position vectors of whose vertices are respectively 7j˙^+10k^, -i˙^+6j˙^+6k^ and -4i˙^+9j˙^+6k^. Then, the ∆ABC is

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

Let $A B C$ be a triangle, the position vectors of whose vertices are respectively $7 \hat{\dot{j}} + 10 \hat{k}, - \hat{\dot{i}} + 6 \hat{\dot{j}} + 6 \hat{k}$ and $- 4 \hat{\dot{i}} + 9 \hat{\dot{j}} + 6 \hat{k}$ . Then, the $∆ A B C$ is