RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

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IMPORTANT

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A unit vector in $X Y$ -plane that makes an angle $45 °$ with the vector $\hat{i} + \hat{j}$ and angle $60 °$ with $3 \hat{i} - 4 \hat{j}$ is

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Important Questions on Vectors

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

A vector perpendicular to

i - j - k

in the plane of

i - j + k

and

i + j + k

is:

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

For two vectors

\vec{a}

and

\vec{b}, {(\vec{a} \cdot \vec{b})}^{2} + {(\vec{a} \times \vec{b})}^{2} =

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IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

The number of unit vectors perpendicular to the vectors

i + j

and

j + k

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

Let three vectors

\vec{a}, \vec{b}, \vec{c}

be coplanar,

\vec{c}

is a unit vector,

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

. If

\vec{c}

is perpendicular to

\vec{a}

then

\vec{c} =

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IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

If sum of two unit vectors is a unit vector, then the angle between them is equal to

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

If

\vec{a}, \vec{b}

are two vectors such that

\vec{a} \cdot \vec{b} < 0

and

|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|

, then the angle between

\vec{a}

and

\vec{b}

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

The vector

\vec{a} + 3 \vec{b}

is perpendicular to

7 \vec{a} - 5 \vec{b}

and

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

is perpendicular to

7 \vec{a} + 3 \vec{b}

; then the angle between

\vec{a}

and

\vec{b}

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 23 - Vectors>EXERCISE>Q 3

If

\vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k}, \vec{b} = 3 \hat{i} + \hat{j} + 2 \hat{k}; \vec{r} = \frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|}

, then

\vec{r} =