If the magnitudes of two vectors a → and b → are equal, then which one of the following is correct?

a → + b → is perpendicular to a → - b →

a → + b → is parallel to a → - b →

a → + b → · a → - b → = 1

If the magnitudes of two vectors a → and b → are equal, then which one of the following is correct?

a → + b → is perpendicular to a → - b →

For two particular vectors A → and B → , it is known that A → × B → = B → × A → . What must be true about the two vectors?

One of the two vectors is a scalar multiple of the other vector

Both vectors must be the zero vector

A → × B → = B → × A → is true for any two vectors

The two vectors must be perpendicular to each other

E M B I B E

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 16

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IMPORTANT

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If the magnitudes of two vectors $\vec{a}$ and $\vec{b}$ are equal, then which one of the following is correct?

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Important Questions on Vector Algebra

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 17

A vector of magnitude

3

, bisecting the angle between the vectors

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

and

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

and making an obtuse angle with

\vec{b}

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 18

If

\vec{a} + \vec{b} + \vec{c} = \vec{0}, |\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7

, then the angle between

\vec{a}

and

\vec{b}

is

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 19

If

| \vec{a} | = 4, | \vec{b} | = 2

and the angle between

\vec{a}

and

\vec{b}

is

\frac{π}{6}

then

{|\vec{a} \times \vec{b}|}^{2}

is equal to

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 20

The moment about the point

\hat{i} + 2 \hat{j} + 3 \hat{k}

of a force represented by

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

acting through the point

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

is

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 21

If the resultant of two forces of magnitudes

P

and

Q

acting at a point at an angle of

60 °

is

\sqrt{13} Q

, then find

\frac{P}{Q}

.

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 22

For two particular vectors

\vec{A}

and

\vec{B}

, it is known that

\vec{A} \times \vec{B} = \vec{B} \times \vec{A}

. What must be true about the two vectors?

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 23

The position vector of a point

P

is

\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}

, where

x, y, z \in N

and

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

. If

\vec{r} \cdot \vec{a}

= 20

, then the number of possible positions of

P

is

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 24

Two adjacent sides of a parallelogram

A B C D

are given by

\vec{A B} = 2 \hat{i} + 10 \hat{j} +11 \hat{k}

and

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

. The side

\vec{A D}

is rotated by an acute angle

α

in the plane of parallelogram so that

\vec{A D}

becomes

\vec{A D^{'}}

. If

\vec{A D^{'}}

makes a right angle with the side

\vec{A B}

, then the cosine of angle

α

is given by

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If the magnitudes of two vectors a→ and b→ are equal, then which one of the following is correct?

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

If the magnitudes of two vectors $\vec{a}$ and $\vec{b}$ are equal, then which one of the following is correct?