Let a-b- be two non collinear unit vectors- If -a-a-b-b-a-b- then

The correct option is A |#160;a|=|#160;β| | β |= | a | | b | sin θ #160; #160; #160; #160; #160; #160; (where θ = angle betw ...

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

Byju's Answer

Standard XII

Mathematics

Relative Position of a Point with Respect to a Line

Let a⃗,b⃗ b...

Question

Let $\to a, \to b$ be two non collinear unit vectors. If $\to α = \to a - (\to a . \to b) \to b, \to β = \to a \times \to b$ , then

| \to a | = | \to β |

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

| \to a |^{2} = | \to β |

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

| \to β |^{2} = | \to α |

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

| \to α | = 2 | \to β |

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

Open in App

Solution

The correct option is A $| \to a | = | \to β |$
$∣ ∣ ∣ \to β ∣ ∣ ∣ = ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ s i n θ$ (where $θ =$ angle between $¯ ¯ ¯ a$ & $¯ ¯ b)$
$= sin θ$
Now,
$∣ ∣ \to α ∣ ∣ = \sqrt{(\to a) + (\to a - \to b)^{2} (\to b)^{2} - 2 (\to a - \to b)^{2}}$
$\sqrt{1 + (\to a \cdot \to b)^{2} - 2 (\to a - \to b)^{2}}$
$= \sqrt{(∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos)^{2}}$
$= sin θ$
So,
$∣ ∣ \to α ∣ ∣ = ∣ ∣ ∣ \to β ∣ ∣ ∣$

Suggest Corrections

Similar questions

Q. If

\to a, \to b, \to c

are non-coplanar vectors and

\to α = \to b \times \to c, \to β = \to c \times \to a, \to r = \to a \times \to b

then

∣ ∣ ∣ ∣ ∣ \begin{matrix} \to α . \to a & \to α . \to b & \to α . \to c \to β . \to a & \to β . \to b & \to β . \to c \to r . \to a & \to r . \to b & \to r . \to c \end{matrix} ∣ ∣ ∣ ∣ ∣ =

Q. Let

\to α = (λ - 2) \to a + \to b

and

\to β = (4 λ - 2) \to a + 3 \to b

be two given vectors where vectors

\to a

and

\to b

are non-collinear. The value of

λ

for which vectors

\to α

and

\to β

are collinear, is:

Q. If a vector

\to a

is expressed as the sum of two vectors

\to α

and

\to β

along and perpendicular to a given vector

\to b

, then

\to β =

Q. If

V

is the volume of parallelepiped formed by the vectors

\to a, \to b, \to c

as three coterminous edges is

27

cubic units, then the volume of the parallelepiped having

\to α = \to a + \to 2 b - \to c, \to β = \to a - \to b

and

\to γ = \to a - \to b - \to c

as three coterminous edges is

Q. Let

\to α, \to β, \to γ

be three unit vectors such that

\to α . \to β = \to α . \to γ = 0.

If the angle between

\to β

and

\to γ

30^{\circ},

then find

\to α

in terms of

\to β

and

\to γ

Join BYJU'S Learning Program

Let →a,→b be two non collinear unit vectors. If →α=→a−(→a.→b)→b,→β=→a×→b, then

Let $\to a, \to b$ be two non collinear unit vectors. If $\to α = \to a - (\to a . \to b) \to b, \to β = \to a \times \to b$ , then