If x- and y- be unit vectors and - z- - 2 - 7 such that z- -z-x- -y- - then the angle - between x- and z- can be

The correct option is A 60 ^∘ We have, z⃗ +z⃗×x⃗ =y⃗ #160; | z⃗ +z⃗×x⃗ #160; | =| y⃗ #160; | =1 | z⃗ +z⃗×x⃗ #160; | ^ 2 =1 ( z⃗ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Addition of Vectors

If x⃗ and ...

Question

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

30^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

60^{\circ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

90^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $60^{\circ}$
We have,
$\to z + \to z \times \to x = \to y | \to z + \to z \times \to x | = | \to y | = 1 {| \to z + \to z \times \to x |}^{2} = 1 (\to z + \to z \times \to x) . (\to z + \to z \times \to x) = 1 \Rightarrow {| \to z |}^{2} + | \to z \times \to x | = 1$
$\frac{4}{7} + \frac{4}{7} {sin}^{2} θ = 1 {sin}^{2} θ = \frac{3}{4} sin θ = \frac{\sqrt{3}}{2} ∴ θ = 60^{o}$

$H e n c e, t h e o p t i o n B i s t h e c o r r e c t a n s w e r .$

Suggest Corrections

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

and

θ

is the angle between

\to x

and

\to z

, then the value of sin

θ

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. 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. 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

Join BYJU'S Learning Program

If →x and →y be unit vectors and |→z|=2√7 such that →z+→z×→x=→y, then the angle θ between →x and →z can be

The correct option is A 60∘We have,→z+→z×→x=→y|→z+→z×→x|=|→y|=1|→z+→z×→x|2=1(→z+→z×→x).(→z+→z×→x)=1⇒|→z|2+|→z×→x|=147+47sin2θ=1sin2θ=34sinθ=√32∴θ=60oHence,theoptionBisthecorrectanswer.

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