Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 74

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JEE Advanced

IMPORTANT

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If vectors $\vec{a}$ and $\vec{b}$ are non-collinear, then $\frac{\vec{a}}{| \vec{a} |} + \frac{\vec{b}}{| \vec{b} |}$

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Important Questions on Product of Vectors

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 75

If

\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{b}) \times \vec{c},

then

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JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 76

Let

\vec{a}

and

\vec{b}

be two non-collinear unit vectors. If

\vec{u} = \vec{a} - (\vec{a} \cdot \vec{b}) \vec{b}

and

\vec{V} = \vec{a} \times \vec{b}

, then

|\vec{V}|

is

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 77

The scalars

l

and

m

such that

l \vec{a} + m \vec{b} = \vec{c}

, where

\vec{a}, \vec{b}

and

\vec{c}

are given vectors, are equal to

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JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 78

Let

\hat{r}

be a unit vector satisfying

\hat{r} \times \vec{a} = \vec{b},

where

|\vec{a}| = \sqrt{3}

and

|\vec{b}| = \sqrt{2}

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JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 79

a_{1}, a_{2}, a_{3} \in R - \{0\}

and

a_{1} + a_{2} \cos 2 x + a_{3} \sin^{2} x = 0

for all

x \in R

, then

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 80

If

\vec{a}

and

\vec{b}

are two vectors and angles between them is

θ

, then

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 81

If unit vectors $\vec{a}$ and $\vec{b}$ are inclined at an angle $2$ $θ$ such that $| \vec{a} - \vec{b} | < 1$ and $0 \leq θ \leq π$ , then $θ$ lies in the interval

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 82

\vec{a}, \vec{b}

and

\vec{c}

are non-collinear if

\vec{a} \times (\vec{b} \times \vec{c}) + (\vec{a} . \vec{b}) \vec{b} = (4 - 2 x - \sin y) \vec{b} + (x^{2} - 1) \vec{c}

and

(\vec{c} . \vec{c}) \vec{a} = \vec{c} .

Then,