Statement -1- The angle between the two vectors - - - and k- is -2 radian-Statement -2- Angle between two vectors A and B is given by - - cos-1 A- B-A-B-

Statement 1: Let, A = î + ĵ and nbsp;B = k̂ So, A. B = |A||B| cosθ ⇒ (î+ĵ).(k̂)=1×1×cosθ ⇒ 0 = cosθ ⇒ θ = π2 Statement 2: A . B = |A||B| cosθ cosθ = A. B| ...

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

Byju's Answer

Standard XIII

Physics

Unit Vectors

Statement -1:...

Question

Statement -1: The angle between the two vectors $(^i +^j)$ and $(^k)$ is $\frac{π}{2}$ radian.
Statement -2: Angle between two vectors $\to A$ and $\to B$ is given by $θ = {cos}^{- 1} ⎛ ⎜ ⎝ \frac{\to A . \to B}{| \to A | | \to B |} ⎞ ⎟ ⎠$

Statement - 1 is True, Statement -2 is True;
Statment -2 is a correct explanation for Statement -1

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

Statement -1 is True, Statement -2 is True;
Statement - 2 is NOT a correct explanation for Statement -1

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

Statement - 1 is True, Statement - 2 is False

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

Statement - 1 is False, Statement - 2 is True

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

Open in App

Solution

The correct option is A Statement - 1 is True, Statement -2 is True;
Statment -2 is a correct explanation for Statement -1
Statement-1:
Let, $\to A =^i +^j$ and $\to B =^k$
So, $\to A . \to B = | \to A | | \to B | cos θ$
$\Rightarrow (^i +^j) . (^k) = 1 \times 1 \times cos θ$
$\Rightarrow 0 = cos θ$
$\Rightarrow θ = \frac{π}{2}$

Statement - 2:
$\to A . \to B = | \to A | | \to B | cos θ$
$cos θ = \frac{\to A . \to B}{| \to A | | \to B |}$

Suggest Corrections

Similar questions

Q. Assertion :The angle between the two vectors

(^i +^j)

and

(^j +^k)

\frac{π}{3}

radian. Reason: Angle between two vectors

\to A

and

\to B

given by

θ = c o s^{- 1} (\frac{\to A . \to B}{A B})

Q. Statement -1: The angle between the two vectors

(^i +^j)

and

(^k)

\frac{π}{2}

radian.
Statement -2: Angle between two vectors

\to A

and

\to B

is given by

θ = {cos}^{- 1} ⎛ ⎜ ⎝ \frac{\to A . \to B}{| \to A | | \to B |} ⎞ ⎟ ⎠

Q. The angle between the two vectors

^i +^j

and

^j +^k

is:

The angle between the vectors $\to a =^i +^j -^k a n d \to b =^i +^j +^k$ is

Q. If

θ

be the angle between the vectors

^i +^j

and

^j +^k

, then

θ

Join BYJU'S Learning Program

Statement -1: The angle between the two vectors (^i+^j) and (^k) is π2 radian. Statement -2: Angle between two vectors →A and →B is given by θ=cos−1⎛⎜⎝→A.→B|→A||→B|⎞⎟⎠

Statement -1: The angle between the two vectors $(^i +^j)$ and $(^k)$ is $\frac{π}{2}$ radian.
Statement -2: Angle between two vectors $\to A$ and $\to B$ is given by $θ = {cos}^{- 1} ⎛ ⎜ ⎝ \frac{\to A . \to B}{| \to A | | \to B |} ⎞ ⎟ ⎠$