Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 60

EASY

JEE Advanced

IMPORTANT

Earn 100

Let us define the length of a vector $a \hat{i} + b \hat{j} + c \hat{k}$ as $|a| + |b| + |c|$ . This definition coincides with the usual definition of length of a vector $a \hat{i} + b \hat{j} + c \hat{k}$ if and only if

50% studentsanswered this correctly

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 61

If

\vec{a} & \vec{b}

are two non-zero and non-collinear vectors, then

\vec{a} + \vec{b} and \vec{a} - \vec{b}

are

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 62

If

|\vec{a} + \vec{b}| < |\vec{a} - \vec{b}|

, then the angle between

\vec{a}

and

\vec{b}

can lie in the interval.

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 63

The magnitudes of mutually perpendicular forces

\vec{a}, \vec{b} and \vec{c}

are

2, 10 and 11

, respectively. Then, the magnitude of its resultant is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 64

If

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

bisects the angle between $\hat{a}$ and

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

, where $\hat{a}$ is a unit vector, then

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 65

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

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

If

\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

is