Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 2

EASY

JEE Main

IMPORTANT

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If a vector $\vec{P}$ is making the angles $α, β$ and $γ$ , respectively, with $X, Y$ and $Z$ axes, then $\sin^{2} α + \sin^{2} β + \sin^{2} γ =$

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Important Questions on Vectors

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 3

If two vectors

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

and

- 4 \hat{i} - 6 \hat{j} + λ \hat{k}

are parallel, then find the value of

λ

.

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 4

The angle between the two vectors,

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

and

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

will be,

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 5

If a vector

2 \hat{i} + 3 \hat{j} + 8 \hat{k}

is perpendicular to the vector

4 \hat{j} - 4 \hat{i} + α \hat{k}

, then the value of

α

is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 6

If for two vectors

\vec{A}

and

\vec{B}

, the sum

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

is perpendicular to the difference

(\vec{A} - \vec{B})

, then the ratio of their magnitude is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 7

Consider a vector

\vec{F} = 4 \hat{i} - 3 \hat{j}

. Another vector which is perpendicular to the

\vec{F}

is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 8

If

|{\vec{V}}_{1} + {\vec{V}}_{2}| = |{\vec{V}}_{1} - {\vec{V}}_{2}|

and

{\vec{V}}_{2}

is finite, then

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 9

The angle between the vectors

(\hat{i} + \hat{j})

and

(\hat{j} + \hat{k})

is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 3 - Vectors>DPP>Q 10

If

\vec{P} \cdot \vec{Q} = P Q

, then the angle between

\vec{P}

and

\vec{Q}

is