Three vectors P → , Q → and R → are shown in the figure. Let, S be any point on the vector R → . The distance between the points P and S is b R → . The general relation among vectors P → , Q → and S → are

S → = 1 - b P → + b 2 Q →

S → = 1 - b 2 P → + b Q →

If in a triangle A B C , A B → = u → u → - v v → → and A C → = 2 u → u → , where u → ≠ v → , then

1 + cos 2 A + cos 2 B + cos 2 C = 0

1 + cos 2 A + cos 2 B + cos 2 C = 3

1 + cos 2 A + cos 2 B + cos 2 C = 4

EASY

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Which is true about negative of a vector?

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Important Questions on Vectors

HARD

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

In a triangle $P Q R$ , let $\vec{a} = \vec{Q R}, \vec{b} = \vec{R P}$ and $\vec{c} = \vec{P Q}$ .

If $|\vec{a}| = 3, |\vec{b}| = 4$ and $\frac{\vec{a} . (\vec{c} - \vec{b})}{\vec{c} . (\vec{a} - \vec{b})} = \frac{|\vec{a}|}{|\vec{a}| + |\vec{b}|}$ , then the value of ${|\vec{a} \times \vec{b}|}^{2}$ is _______

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Two forces

P

and

Q

, of magnitude

2 F

and

3 F

, respectively, are at an angle

θ

with each other. If the force

Q

is doubled, then their resultant also gets doubled. Then, the angle

θ

is:

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}, \vec{B} = \hat{i} - 3 \hat{j} + 5 \hat{k}

and

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

form a right angled triangle then out of the following which one is satisfied?

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

In a

∆ A B C,

D, E, F

are the mid-points of the sides

B C

C A

and

A B

respectively, the vector

\vec{A D}

is equal to

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Let

\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + 2 \hat{j} + \hat{k}

and

\vec{c} = 5 \hat{i} + \hat{j} - \hat{k}

be three vectors. The area of the region formed by the set of points whose position vectors

\vec{r}

satisfy the equations

\vec{r} \cdot \vec{a} = 5

and

| \vec{r} - \vec{b} | + | \vec{r} - \vec{c} | = 4

is closest to the integer.

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

A unit vector is represented as

(0 .8 \hat{i} + b \hat{j} + 0 .4 \hat{k})

. Hence the value of

b

must be

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

\vec{a}

is a nonzero vector of magnitude

‘ a ’

and

λ

a nonzero scalar then

λ \vec{a}

is unit vector if

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Number of unit vectors of the form

a \hat{i} + b \hat{j} + c \hat{k},

where

a, b, c \in W

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

The two vectors

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

and

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

represent the two sides

\vec{A B}

and

\vec{A C}

respectively of a

Δ A B C

. The length of the median through

A

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

\vec{P} and \vec{Q}

are two non-zero vectors inclined to each other at an angle

θ .

\hat{p} and \hat{q}

are unit vectors along

\vec{P} a n d \vec{Q}

respectively. The component of

\vec{Q}

in the direction of

\vec{P}

will be

HARD

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Three vectors

\vec{P}, \vec{Q}

and

\vec{R}

are shown in the figure. Let,

S

be any point on the vector

\vec{R}

. The distance between the points

P

and

S

b |\vec{R}|

. The general relation among vectors

\vec{P}, \vec{Q}

and

\vec{S}

are

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

If 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

Δ A B C

, then the length of the median through

A

is-

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Let

A B C

be a triangle, the position vectors of whose vertices are respectively

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

and

- 4 \hat{\dot{i}} + 9 \hat{\dot{j}} + 6 \hat{k}

. Then, the

∆ A B C

MEDIUM

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

Mark the correct statement?

HARD

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

If in a triangle

A B C, \vec{A B} = \frac{\vec{u}}{|\vec{u}|} - \vec{\frac{v}{|\vec{v}|}}

and

\vec{A C} = \frac{2 \vec{u}}{|\vec{u}|}

, where

|\vec{u}| \neq |\vec{v}|

, then

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

G

is the centroid of the

∆ A B C,

then

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

is equal to

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

The ratio in which the line joining

(2, 4, 5)

(3,5, - 4)

is divided by the

y z

-plane is

HARD

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

\vec{p}, \vec{q}

and

\vec{r}

are perpendicular to

\vec{q} + \vec{r}, \vec{r} + \vec{p}

and

\vec{p} + \vec{q}

respectively and if

|\vec{p} + \vec{q}| = 6, |\vec{q} + \vec{r}| = 4 \sqrt{3}

and

|\vec{r} + \vec{p}| = 4,

then

| \vec{p} + \vec{q} + \vec{r} |

EASY

Mathematics (9709)>P-3: Pure Mathematics 3>Vectors>Addition and Subtraction of Vectors

The point in the

x y

-plane which is equidistant from the points (2,0,3), (0,3,2) and (0,0,1) is

Which is true about negative of a vector?

Which is true about negative of a vector?

Important Questions on Vectors

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