If a → , b → , c → are the vectors of which every pair is noncollinear. If the vector a → + b → and b → + c → are collinear with c → and a → respectively, then a → + b → + c → is

equally inclined to a → , b → , c →

HARD

MHT-CET

IMPORTANT

Earn 100

If the volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}$ and $\vec{c}$ is $4$ , then the volume of the parallelepiped formed by the coterminous edges $\vec{a} \times \vec{b}, \vec{b} \times \vec{c}$ and $\vec{c} \times \vec{a}$ is

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Important Questions on Vectors

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 70

The volume of the parallelepiped whose edges are represented by

- 12 \hat{i} + α \hat{k}, 3 \hat{j} - \hat{k}

and

2 \hat{i} + \hat{j} - 15 \hat{k}

546

cu. units, then

α =

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 74

The vectors

\vec{A B} = 3 \hat{i} + 5 \hat{j} + 4 \hat{k}

and

\vec{A C} = 5 \hat{i} - 5 \hat{j} + 2 \hat{k}

are the sides of a triangle

A B C

. The length of the median through

A

MEDIUM

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 75

A (4, 3, 5), B (0, - 2, 2)

and

C (3, 2, 1)

are three points. The coordinates of the point in which the bisector of

∠ B A C

meets the side

\bar{B C}

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 76

4 \hat{i} + 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 triangle

A B C

. The position vector of the point where the bisector of angle

A

meets

B C

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 77

Consider points

A, B, C

and

D

with position vectors

7 \hat{i} - 4 \hat{j} + 7 \hat{k}, \hat{i} - 6 \hat{j} + 10 k, - \hat{i} - 3 \hat{j} + 4 \hat{k}

and

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

, respectively. Then,

A B C D

is a

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Competitive Thinking>Q 78

In a right

-

angled triangle

A B C

, the hypotenuse

A B = p

. Then,

(\vec{A B} \cdot \vec{A C} + \vec{B C} \cdot \vec{B A} + \vec{C A} \cdot \vec{C B})

is equal to

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Evaluation Test>Q 1

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

are the vectors of which every pair is noncollinear. If the vector

\vec{a} + \vec{b}

and

\vec{b} + \vec{c}

are collinear with

\vec{c}

and

\vec{a}

respectively, then

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

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Evaluation Test>Q 2

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

are three non-coplanar vectors such that

{\vec{r}}_{1} = \vec{a} - \vec{b} + \vec{c}, {\vec{r}}_{2} = \vec{b} + \vec{c} - \vec{a}, {\vec{r}}_{3} = \vec{c} + \vec{a} + \vec{a}, \vec{r} = 2 \vec{a} - 3 \vec{b} + 4 \vec{c}

. If

\vec{r} = λ_{1} {\vec{r}}_{1} + λ_{2} {\vec{r}}_{2} + λ_{3} {\vec{r}}_{3}

, then

If the volume of the tetrahedron formed by the coterminous edges a→, b→ and c→ is 4, then the volume of the parallelepiped formed by the coterminous edges a→×b→, b→×c→ and c→×a→ is

Important Questions on Vectors

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If the volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}$ and $\vec{c}$ is $4$ , then the volume of the parallelepiped formed by the coterminous edges $\vec{a} \times \vec{b}, \vec{b} \times \vec{c}$ and $\vec{c} \times \vec{a}$ is