If b → is a vector whose initial point divides the join of 5 i ^ and 5 j ^ in the ratio k : 1 and whose terminal point is origin and b → ≤ 37 , then k lies in the interval

( – ∞ , – 6 ] ∪ [ – 1 6 , ∞ )

EASY

JEE Advanced

IMPORTANT

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Let $\vec{a} = \hat{i}$ be a vector which makes an angle of $120 °$ with a unit vector $\vec{b}$ . Then, the unit vector $(\vec{a} + \vec{b})$ 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 1>Q 66

Given three vectors

\vec{a} = 6 \hat{i} - 3 \hat{j}

\vec{b} = 2 \hat{i} - 6 \hat{j}

and

\vec{c} = - 2 \hat{i} + 21 \hat{j}

such that

\vec{α} = \vec{a} + \vec{b} + \vec{c}

. Then, the resolution of the vector

\vec{α}

into components with respect to

\vec{a}

and

\vec{b}

is given by

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 67

{}^{'}I^{'}

is the incentre of

Δ A B C

whose corresponding sides are

a, b, c

, respectively.

a Ι A + b Ι B + c Ι C

is always 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 68

\vec{X} and \vec{Y}

are two non-collinear vectors and

A B C

is a triangle with side lengths

a, b

and

c

satisfying

(20 a -15 b) \vec{X} + (15 b -12 c) \vec{Y} + (12 c - 20 a) (\vec{X} \times \vec{Y}) =0

, then

Δ A B C

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 69

\vec{X} and \vec{Y}

are two non-collinear vectors and

a, b and c

represent the sides of a

Δ A B C

satisfying

(a - b) \vec{X} + (b - c) \vec{Y} + (c - a) (\vec{X} \times \vec{Y}) =0

, then

Δ A B C

is (where

\vec{X} \times \vec{Y}

is perpendicular to the plane of

\vec{X}

and

\vec{Y}

)

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 70

If the resultant of two forces is of magnitude

|\vec{P}|

and equal to one of them and perpendicular to it, then the other force is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 71

\vec{b}

is a vector whose initial point divides the join of

5 \hat{i}

and

5 \hat{j}

in the ratio

k : 1

and whose terminal point is origin and

|\vec{b}|

\leq \sqrt{37}

, then

k

lies in the interval

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 72

4 \hat{j} + 7 \hat{j} + 8 \hat{k}, 2 \hat{i} + 3 \hat{j} + 4 \hat{k}

and

2 \hat{i} + 5 \hat{j} + 7 \hat{k}

are the position vectors of the vertices

A, B and C

, respectively of

Δ A B C

. The position vector of the point where the bisector of

∠ A

meets

\vec{B C}

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 73

\vec{a} & \vec{b}

are two unit vectors and

θ

is the angle between them, then the unit vector along the angular bisector of

\vec{a} and \vec{b}

will be given by

Let a→=i^ be a vector which makes an angle of 120° with a unit vector b→. Then, the unit vector a→+b→ is

Important Questions on Vector Algebra

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Let $\vec{a} = \hat{i}$ be a vector which makes an angle of $120 °$ with a unit vector $\vec{b}$ . Then, the unit vector $(\vec{a} + \vec{b})$ is