Choose the correct answer If - is the angle between any two vectors a and b- then - a - b - a - b - when - is equal toa Zerob -4c 1-2d -

We have |a· b|=|a × b| ⇒ |a| |b| cos θ = |a| |b| sin θ nbsp; ⇒cos θ = sin θ nbsp; nbsp; [|a| and |b| are positive] ⇒tan θ = 1 ⇒tan θ = tanπ/4 ⇒θ = π/4H ...

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Standard XII

Physics

Multiplication with Vectors

Choose the co...

Question

Choose the correct answer
If $θ$ is the angle between any two vectors a and b, then $| a \cdot b | = | a \times b |$ , when $θ$ is equal to
a) Zero
b) $\frac{π}{4}$
c) $\frac{π}{2}$
d) $π$

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Solution

We have $| a \cdot b | = | a \times b | \Rightarrow | a | | b | cos θ = | a | | b | sin θ$
$\Rightarrow cos θ = sin θ$ [ $| a |$ and $| b |$ are positive]
$\Rightarrow tan θ = 1 \Rightarrow tan θ = tan \frac{π}{4} \Rightarrow θ = \frac{π}{4}$
Hence, the value of $θ = \frac{π}{4}$ .

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Similar questions

Q. If θ is the angle between any two vectors

\vec{a} and \vec{b}

, then

|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|

when θ is equal to

(a) 0
(b) π/4
(c) π/2
(d) π

Q. If θ is the angle between any two vectors and , then when θ isequal to (A) 0 (B) (C) (D) π

Choose the correct answer
Let a and b be two unit vectors and $θ$ is the angle between them. Then, a + b is a unit vector, if

a) $θ = \frac{π}{4}$
b) $θ = \frac{π}{3}$
c) $θ = \frac{π}{2}$
d) $θ = \frac{2 π}{3}$

If θ is the angle between any two vectors and, then when θisequal to

(A) 0 (B) (C) (D) π

Choose the correct answer
If $θ$ is the angle between two vectors a and b, then $a . b \geq 0$ only when
a) $0 < θ < \frac{π}{2}$
b) $0 \leq θ < \frac{π}{2}$
c) $0 < θ < π$
d) $0 \leq θ \leq π$

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Choose the correct answer If θ is the angle between any two vectors a and b, then |a⋅b|=|a×b|, when θ is equal to a) Zero b) π4 c) π2 d) π

We have |a⋅b|=|a×b|⇒|a||b|cos θ=|a||b| sin θ ⇒cos θ=sin θ [|a| and |b| are positive] ⇒tan θ=1⇒tan θ=tanπ4⇒θ=π4Hence, the value of θ=π4.

Choose the correct answer
If $θ$ is the angle between any two vectors a and b, then $| a \cdot b | = | a \times b |$ , when $θ$ is equal to
a) Zero
b) $\frac{π}{4}$
c) $\frac{π}{2}$
d) $π$

We have $| a \cdot b | = | a \times b | \Rightarrow | a | | b | cos θ = | a | | b | sin θ$
$\Rightarrow cos θ = sin θ$ [ $| a |$ and $| b |$ are positive]
$\Rightarrow tan θ = 1 \Rightarrow tan θ = tan \frac{π}{4} \Rightarrow θ = \frac{π}{4}$
Hence, the value of $θ = \frac{π}{4}$ .