Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 11

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IMPORTANT

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The horizontal force and the force inclined at an angle $60^{\circ}$ with the vertical, whose resultant is in vertical direction of $P kg$ , are

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Important Questions on Vector Algebra

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 12

Let

\vec{α} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{β} = 2 \hat{i} - \hat{j} + 3 \hat{k}

and

\vec{γ} = 2 \hat{i} + \hat{j} + 6 \hat{k}

be three vectors. If

\vec{α}

and

\vec{β}

are both perpendicular to the vector

\vec{δ}

and

\vec{δ} \cdot \vec{γ} = 10

, then what is the magnitude of

\vec{δ}

?

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 13

If

\vec{a}

and

\vec{b}

are vectors such that

| \vec{a} | = 2,

| \vec{b} | = 7

and

\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k},

then what is the acute angle between

a

and

b

?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 14

Let

\vec{p}

and

\vec{q}

be the position vectors of the points

P

and

Q

respectively, with respect to origin

O .

The points

R

and

S

divide

P Q

internally and externally respectively, in the ratio

2 : 3 .

If

\vec{O R}

and

\vec{O S}

are perpendicular, then which one of the following is correct?

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 15

If

| \vec{a} | = 3, | \vec{b} | = 4

and

| \vec{a} - \vec{b} | = 5

, then what is the value of

| \vec{a} + \vec{b} | ?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 16

Let

\vec{a}, \vec{b}

and

\vec{c}

be three mutually perpendicular vectors each of unit magnitude. If

\vec{A} = \vec{a} + \vec{b} + \vec{c}, \vec{B} = \vec{a} - \vec{b} + \vec{c}

and

\vec{C} = \vec{a} - \vec{b} - \vec{c}

, then which one of the following is correct?

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 17

If

\vec{a}, \vec{b}

and

\vec{c}

are three mutually perpendicular vectors of equal magnitude, then the angle

θ

which

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

makes with any one of three given vectors is given by

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 18

If

|\vec{a}| = 3, |\vec{b}| = 4

and

|\vec{c}| = 5

such that each is perpendicular to sum of the other two, then

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

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 19

If

\vec{a}

and

\vec{b}

are unit vectors and

θ

is the angle between them, then

\sin (\frac{θ}{2})

is equal to