Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 82

HARD

JEE Advanced

IMPORTANT

Earn 100

$O A B C D E$ is a regular hexagon of side $2$ units in the $X Y$ -plane. $O$ being the origin and $O A$ taken along the positive $X$ -axis. A point $P$ is taken on a line parallel to $Z$ -axis through the centre of the hexagon at a distance of $3$ units from $O .$ Then, the vector $\vec{A P}$ is

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Important Questions on Vector Algebra

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 83

If the vectors

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

and

\vec{a}

form a triangle, then

\vec{a}

may be

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JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 84

If the resultant of three forces

\vec{F_{1}} = p \hat{i} + 3 \hat{j} - \hat{k}, \vec{F_{2}} = 6 \hat{i} - \hat{k}

and

\vec{F_{3}} = - 5 \hat{i} + \hat{j} + 2 \hat{k}

acting on a particle has a magnitude equal to

5

units, then the value of

p

is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 85

Let

A B C

be a triangle, the position vectors whose vertices are

7 \hat{j} + 10 \hat{k}, - \hat{i} + 6 \hat{j} + 6 \hat{k}

and

- 4 \hat{i} + 9 \hat{j} + 6 \hat{k}

. Then,

Δ A B C

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 86

The sides of a parallelogram are

2 \hat{i} + 4 \hat{j} - 5 \hat{k}

and

\hat{i} + 2 \hat{j} + 3 \hat{k}

. The unit vector parallel to one of the diagonals is

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 87

If

A (- 4, 0, 3)

and

B (14, 2, - 5)

, then which one of the following points lies on the bisector of the angle between

\vec{O A}

and

\vec{O B}

(

O

is the origin of reference)?

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 88

If point

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

and

p \hat{i} + q \hat{j} + r \hat{k}

are collinear, then

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 2>Q 89

If

\vec{a}, \vec{b}

and

\vec{c}

are non-coplanar vectors and

λ

is a real number, then the vectors

(\vec{a} + 2 \vec{b} + 3 \vec{c}), (λ \vec{b} + μ \vec{c})

and

(2 λ - 1) \vec{c}

are coplanar when

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 7>Q 112

A vector

\vec{a}

has components

{\vec{a}}_{1}, {\vec{a}}_{2} & {\vec{a}}_{3}

in a right-handed rectangular Cartesian system

O X Y Z

. The coordinate system is rotated about

Z

-axis through the angle

\frac{π}{2}

. Find the components of

\vec{a}

in new system.