EASY

Earn 100

Explain radius vector.

Important Questions on Vector Algebra

MEDIUM

Mathematics>Coordinate 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.

MEDIUM

Mathematics>Coordinate 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}

MEDIUM

Mathematics>Coordinate 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}

EASY

Mathematics>Coordinate 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>Coordinate 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>Coordinate 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:

MEDIUM

Mathematics>Coordinate 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>Coordinate Geometry>Vector Algebra>Basics of Vectors

Let

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{j} - 3 \hat{k} .

\vec{b} = \vec{c} - \vec{d}, \vec{a}

is parallel to

\vec{c}

and perpendicular to

\vec{d}

, then

\vec{c} + \vec{d} =

EASY

Mathematics>Coordinate Geometry>Vector Algebra>Basics of Vectors

The direction cosines of the vector

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

are

EASY

Mathematics>Coordinate 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>Coordinate 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>Coordinate 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>Coordinate 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>Coordinate 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>Coordinate 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>Coordinate Geometry>Vector Algebra>Basics of Vectors

The point of intersection of the lines joining points

\hat{i} + 2 \hat{j}, 2 \hat{i} - \hat{j}

and

- \hat{i}, 2 \hat{i}

MEDIUM

Mathematics>Coordinate Geometry>Vector Algebra>Basics of Vectors

Let

\vec{u} = 2 \hat{i} + \hat{j}

and

\vec{v} = 3 \hat{i} - 5 \hat{j}

. Consider three points

P, Q

and

R

having the position vectors

(\frac{5}{2}) \hat{i} - 2 \hat{j}, (\frac{7}{3}) \hat{i} - \hat{j}

and

(\frac{9}{4}) \hat{i}

respectively. Among these, the points in the line passing through

\vec{u}

and

\vec{v}

are

MEDIUM

Mathematics>Coordinate 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

HARD

Mathematics>Coordinate Geometry>Vector Algebra>Basics of Vectors

Let

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

and

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

be two vectors. Consider a vector

\vec{c} = α \vec{a} + β \vec{b}, α, β \in R .

If the projection of

\vec{c}

on the vector

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

3 \sqrt{2},

then the minimum value of

(\vec{c} - (\vec{a} \times \vec{b})) . \vec{c}

equals

EASY

Mathematics>Coordinate 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

Explain radius vector.

Important Questions on Vector Algebra

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