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JEE Advanced

IMPORTANT

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On the $x y$ plane where $O$ is the origin, given points, $A (1, 0), B (0, 1)$ and $C (1, 1)$ . Let $P, Q and R$ be moving point on the line $\vec{O A}, \vec{O B}, \vec{O C}$ , respectively such that $\vec{O P} = 45 t (\vec{O A}), \vec{O Q} = 60 t (\vec{O B}), \vec{O R} = (1 - t) (\vec{O C})$ with $t > 0$ . If the three points $P, Q and R$ are collinear, then the value of $t$ is equal to

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Important Questions on Vector Algebra

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 76

\vec{a}, \vec{b}

and

\vec{c}

are three non-coplanar vectors such that

\vec{a} + \vec{b} + \vec{c} = α \vec{d}

and

\vec{b} + \vec{c} + \vec{d} = β \vec{a}

, then

\vec{a} + \vec{b} + \vec{c} + \vec{d}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 77

The position vectors of the points

P

and

Q

with respect to the origin

O

are

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

and

\vec{b} = 3 \hat{i} - \hat{j} - 2 \hat{k}

, respectively. If

M

is a point on

\vec{P Q}

, such that

\vec{O M}

is the bisector of

∠ P O Q

, then

\vec{O M}

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 78

A B C D

is a quadrilateral.

E

is the point of intersection of the line joining the midpoints of the opposite sides. If

O

is any point and

\vec{O A} + \vec{O B} + \vec{O C} + \vec{O D} = x \vec{O E}

, then

x

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 79

In the

Δ O A B

M

is the mid-point of

\vec{A B}

C

is a point on

\vec{O M}

, such that

2 \vec{O C} = \vec{C M}

X

is a point on the side

\vec{O B}

such that

\vec{O X} = 2 \vec{X B}

. The line

\vec{X C}

is produced to meet

\vec{O A}

Y

. Then,

\frac{\vec{O Y}}{\vec{Y A}}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 80

Points

X and Y

are taken on the sides

\vec{Q R} and \vec{R S}

, respectively of a parallelogram

P Q R S

, so that

\vec{Q X} = 4 \vec{X R} and \vec{R Y} = 4 \vec{Y S}

. The line

\vec{X Y}

cuts the line

\vec{P R}

Z

. Then,

\vec{P Z}

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 81

Find the value of

λ

so that the points

P, Q, R and S

on the sides

\vec{O A}, \vec{O B}, \vec{O C} and \vec{A B}

, respectively, of a regular tetrahedron

O A B C

are coplanar. It is given that

\frac{\vec{O P}}{\vec{O A}} = \frac{1}{3}, \frac{\vec{O Q}}{\vec{O B}} = \frac{1}{2}, \frac{\vec{O R}}{\vec{O C}} = \frac{1}{3} and \frac{\vec{O S}}{\vec{A B}} = λ

HARD

JEE Advanced

IMPORTANT

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

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}

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

On the xy plane where O is the origin, given points, A1,0, B0,1 and C1,1. Let P,Q and R be moving point on the line OA→,OB→,OC→, respectively such that OP→=45tOA→, OQ→=60tOB→, OR→=1-tOC→ with t>0. If the three points P, Q and R are collinear, then the value of t is equal to

Important Questions on Vector Algebra

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