If x- and y- be unit vectors and -z- - 2-7 such that z- - z-x- - y- and - is the angle between x- and z- then the value of sin - is

The correct option is A √(3)2 |z⃗ + (z⃗×x⃗) | = | y⃗|^2 ⇒ |z⃗|^2+|z⃗|^2 |x⃗|^2 sin^2 θ =1 ⇒ |z| = 1/√(1 + sin^2 θ) = 2/√(7)⇒ sin θ = ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

If x⃗ and ...

Question

If $\to x$ and $\to y$ be unit vectors and $| \to z | = \frac{2}{\sqrt{7}}$ such that $\to z + (\to z \times \to x) = \to y$ and $θ$ is the angle between $\to x$ and $\to z$ , then the value of sin $θ$ is

\frac{1}{2}

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1

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\frac{\sqrt{3}}{2}

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\frac{\sqrt{3} - 1}{2 \sqrt{2}}

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Solution

The correct option is A $\frac{\sqrt{3}}{2}$
$| \to z + (\to z \times \to x) | = | \to y |^{2} \Rightarrow$
$| \to z |^{2} + | \to z |^{2} | \to x |^{2} s i n^{2} θ = 1$
$\Rightarrow | z | = \frac{1}{\sqrt{1 + s i n^{2} θ}} = \frac{2}{\sqrt{7}} \Rightarrow s i n θ = \frac{\sqrt{3}}{2}$

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Similar questions

Q. If

\to x

and

\to y

be unit vectors and

| \to z | = \frac{2}{\sqrt{7}}

such that

\to z + \to z \times \to x = \to y,

then the angle

θ

between

\to x

and

\to z

can be

Q. Let

\to x, \to y

and

\to z

be unit vectors such that

\to x + \to y + \to z = \to a, \to x \times (\to y \times \to z) = \to b, (\to x \times \to y) \times \to z = \to c

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2

.

Then which of the following option(s) is/are CORRECT ?

Q. Vector

\to x

is Vectors

\to x, \to y

and

\to z,

each of magnitude

\sqrt{2},

make an angle of

60^{\circ}

with each other.

\to x \times (\to y \times \to z) = \to a, \to y \times (\to z \times \to x) = \to b

and

\to x \times \to y = \to c .

Q. If

\to x, \to y, \to z

are units vectors such that

\to x + \to y + \to z = \to a

(\to x \times \to y) \times \to z = \to b

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2,

then which of the following is FALSE?

Q. If

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

and

\to y \cdot \to z = 1

. Vector

\to z

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If →x and →y be unit vectors and |→z|=2√7 such that →z+(→z×→x)=→y and θ is the angle between →x and →z, then the value of sin θ is

The correct option is A √32|→z+(→z×→x)|=|→y|2⇒|→z|2+|→z|2|→x|2sin2θ=1⇒|z|=1√1+sin2θ=2√7⇒sinθ=√32

If $\to x$ and $\to y$ be unit vectors and $| \to z | = \frac{2}{\sqrt{7}}$ such that $\to z + (\to z \times \to x) = \to y$ and $θ$ is the angle between $\to x$ and $\to z$ , then the value of sin $θ$ is

The correct option is A $\frac{\sqrt{3}}{2}$
$| \to z + (\to z \times \to x) | = | \to y |^{2} \Rightarrow$
$| \to z |^{2} + | \to z |^{2} | \to x |^{2} s i n^{2} θ = 1$
$\Rightarrow | z | = \frac{1}{\sqrt{1 + s i n^{2} θ}} = \frac{2}{\sqrt{7}} \Rightarrow s i n θ = \frac{\sqrt{3}}{2}$