Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 44

EASY

JEE Advanced

IMPORTANT

Earn 100

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $3 \vec{a} + 4 \vec{b} + 5 \vec{c} = 0$ , then which of the following statements is true?

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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 1>Q 45

A, B, C, D

and

E

are five coplanar points, then

\vec{D A} + \vec{D B} + \vec{D C} + \vec{A E} + \vec{B E} + \vec{C E}

is equal to

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 46

If the vectors

\vec{a}

and

\vec{b}

are linearly independent satisfying

(\sqrt{3} \tan θ +1) \vec{a} + (\sqrt{3} \sec θ -2) \vec{b} = 0

, then the most general value of

θ

are

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 47

The unit vector bisecting

\vec{O Y}

and

\vec{O Z}

is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 48

A line passes through the points whose position vectors are

\hat{i} + \hat{j} - 2 \hat{k}

and

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

. The position vector of a point on it at unit distance from the first point is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 49

If

D, E and F

are the midpoints of the sides

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

of the

∆ A B C

, then

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

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 50

If

P and Q

are the middle points of the sides

\vec{B C} and \vec{C D}

of the parallelogram

A B C D

, then

\vec{A P} + \vec{A Q}

is equal to

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 51

The figure formed by the four points

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

,

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

,

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

and

\hat{k} - \hat{j}

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 52

A and B

are two points. The Position Vector of

A

is

6 \vec{b} - 2 \vec{a}

. A Point

P

divides the line

\vec{A B}

in the ratio

1 : 2 .

If

\vec{a} - \vec{b}

is the position vector of

P

, then the position vector of

B

is given by