The position vectors of the points A , B , and C are i ^ + 2 j ^ − k ^ , i ^ + j ^ + k ^ and 2 i ^ + 3 j ^ + 2 k ^ , respectively. If A is chosen as the origin, then the position vectors of B and C are

- j ^ + 2 k ^ , i ^ + j ^ + 3 k ^

i ^ + 2 k ^ , i ^ + j ^ + 3 k ^

j ^ + 2 k ^ , i ^ + j ^ + 3 k ^

- j ^ + 2 k ^ , i ^ - j ^ + 3 k ^

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 11

HARD

JEE Main

IMPORTANT

Earn 100

In a regular hexagon $A B C D E F$ , $\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} = k \vec{AD}$ , where $k$ is equal to

60% studentsanswered this correctly

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 12

If

\vec{a} + \vec{b} + \vec{c} = \vec{0}

and

|\vec{a}| = 3, |\vec{b}| = 5

and

|\vec{c}| = 7

, then the angle between

\vec{a}

and

\vec{b}

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Vectors and 3D Geometry JEE Main & Advanced>Chapter 1 - Introduction to Vectors>DPP>Q 13

If the sum of two unit vectors is a unit vector, then the magnitude of their difference 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 14

The position vectors of the points $A, B$ , and $C$ are $\hat{i} + 2 \hat{j} - \hat{k}$ , $\hat{i} + \hat{j} + \hat{k}$ and $2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ , respectively. If $A$ is chosen as the origin, then the position vectors of $B$ and $C$ are