Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 15

MEDIUM

JEE Main

IMPORTANT

Earn 100

The orthocentre of an equilateral triangle $A B C$ is the origin $O$ . If $\vec{O A} = \vec{a}$ , $\vec{O B} = \vec{b}$ and $\vec{O C} = \vec{c}$ , then $\vec{A B} + 2 \vec{B C} + 3 \vec{C A}$ is equal to

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Important Questions on Introduction to Vectors

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 16

If the position vectors of

P

and

Q

are

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

and

5 \hat{i} - 3 \hat{j} + 4 \hat{k}

, respectively, then the cosine of the angle between

\vec{P Q}

and

z

-axis is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 17

The non-zero vectors

\vec{a}

,

\vec{b}

and

\vec{c}

are related by

\vec{a} = 8 \vec{b}

and

\vec{c} = - 7 \vec{b}

, the angle between

\vec{a}

and

\vec{c}

is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 18

The unit vector bisecting

\vec{O Y}

(representing

Y

-axis) and

\vec{O Z}

(representing

Z

- axis) is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 19

A unit tangent vector at

t = 2

on the curve

x = t^{2} + 2

,

y = 4 t - 5

and

z = 2 t^{2} - 6 t

is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 20

If $\vec{a}$ and $\vec{b}$ are the position vectors of $A$ and $B$ , respectively, then the position vector of a point $C$ is $\vec{A B}$ , produced such that $\vec{A C} = 2015 \vec{A B}$ .

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 21

Let

\vec{a} = (1, 1, - 1)

,

\vec{b} = (5, - 3, - 3)

and

\vec{c} = (3, - 1, 2)

. If

\vec{r}

is collinear with

\vec{c}

and has length of

\frac{|\vec{a} + \vec{b}|}{2}

, then

\vec{r}

equals

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 22

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 the line at unit distance from the first point can be

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 1

The number of integral values of

p

for which

(p + 1) \hat{i} - 3 \hat{j} + p \hat{k}, p \hat{i} + (p + 1) \hat{j} - 3 \hat{k}

and

- 3 \hat{i} + p \hat{j} + (p + 1) \hat{k}

are linearly dependent vectors is/are