Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 2

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If $\vec{a}$ and $\vec{b}$ are position vectors of $A$ and $B$ respectively, then the position vector of a point $C$ in $A B$ produced such that $\vec{A C} = 3 \vec{A B}$ is

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Important Questions on Vector Algebra

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 3

If

S

is the circumcentre,

O

is the orthocentre of

∆ A B C

, then

\vec{SA} + \vec{SB} + \vec{SC}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 4

If

G

and

G^{'}

are the centroids of the triangles

A B C

and

A^{'} B^{'} C^{'},

then

\vec{A A'} + \vec{B B'} + \vec{C C'}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 5

Let

A B C D E F

be a regular hexagon. If

\vec{A D} = x \vec{B C}

and

\vec{C F} = y \vec{A B},

then

x y =

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 6

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

and

\vec{A C} = \hat{i} - \hat{j} + 3 \hat{k} .

If the point

P

on the line segment

B C

is equidistant from

A B

and

A C,

then

\vec{A P}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 7

If the vectors

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

and

\vec{A C} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}

are the sides of a triangle

A B C,

then the length of the median through

A

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 8

A, B, C, D

and

E

are five coplanar points, then

\vec{D A} + \vec{D B} + \vec{D C} + \vec{A E} + \vec{B E} + \vec{C E}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 9

The vectors

\hat{i} + \hat{j}, \hat{j} + \hat{k}

and

\hat{k} + \hat{i}

are

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.1>Q 10

Let

α, β

and

γ

be the distinct real numbers. The points with position vectors

α \hat{i} + β \hat{j} + γ \hat{k}, β \hat{i} + γ \hat{j} + α \hat{k}

and

γ \hat{i} + α \hat{j} + β \hat{k}

forms