If the angle - between the vectors a -2 x 2-4 x -k- and b -7 -2 - x k- is such that 90-180-then x lies in the interval-A- 1-2- 1B- 0- 1-2C- 1- 3-2D- 1-2- 3-2

The correct option is B ( 0, 1/2 )90^∘ lt; θ lt; 180^∘⇒ a.b lt; 0 ⇒ (2x^2î+4xĵ+k̂).(7î 2ĵ+xk̂) lt;0 ⇒ 14x^2 8x +x lt; 0 ⇒ 14x^2 7x lt; 0 ⇒ 7x (2 ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Vectors

If the angle ...

Question

If the angle θ between the vectors $a = 2 x^{2}^i + 4 x^j +^k$ and $b = 7^i - 2^j + x^k$ is such that $90^{\circ}$ < $θ$ < $180^{\circ}$
then x lies in the interval:

(0, \frac{1}{2})

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(\frac{1}{2}, 1)

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(1, \frac{3}{2})

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(\frac{1}{2}, \frac{3}{2})

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Solution

The correct option is A $(0, \frac{1}{2})$
$90^{\circ} < θ < 180^{\circ} \Rightarrow a . b < 0 \Rightarrow (2 x^{2}^i + 4 x^j +^k) . (7^i - 2^j + x^k) < 0 \Rightarrow 14 x^{2} - 8 x + x < 0 \Rightarrow 14 x^{2} - 7 x < 0 \Rightarrow 7 x (2 x - 1) < 0 \Rightarrow 0 < x < \frac{1}{2}$

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Similar questions

Q. If the angle θ between the vectors

a = 2 x^{2}^i + 4 x^j +^k

and

b = 7^i - 2^j + x^k

is such that

90^{\circ}

θ

180^{\circ}

then x lies in the interval:

Q. If the angle θ between the vectors

a = 2 x^{2}^i + 4 x^j +^k

and

b = 7^i - 2^j + x^k

is such that

90^{\circ}

θ

180^{\circ}

then x lies in the interval:

Q. Find the value of

x

for which the angle between the vectors

^a = 2 x^{2}^i + 4 x^j +^k

and

^b = 7^i - 2^j + x^k

is obtuse.

Q. The values of

x

for which the angle between the vectors

2 x^{2}^i + 4 x^j +^k

and

7^i - 2^j + x^k

are obtuse and the angle between the

z -

axis and

7^i - 2^j + x^k

is acute and less than

\frac{π}{6}

is given by

Q. The values of

x

for which the angle between

\to a = 2 x^{2}^i + 4 x^j +^k

and

\to b = 7^i - 2^j + x^k

is obtuse and the angle between

\to b

and the

z

-axis is acute and less than

\frac{π}{6}

, are

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If the angle θ between the vectors a=2x2^i+4x^j+^k and b=7^i−2^j+x^k is such that 90∘ < θ < 180∘ then x lies in the interval:

The correct option is A (0,12)90∘<θ<180∘⇒a.b<0⇒(2x2^i+4x^j+^k).(7^i−2^j+x^k)<0⇒14x2−8x+x<0⇒14x2−7x<0⇒7x(2x−1)<0⇒0<x<12

If the angle θ between the vectors $a = 2 x^{2}^i + 4 x^j +^k$ and $b = 7^i - 2^j + x^k$ is such that $90^{\circ}$ < $θ$ < $180^{\circ}$
then x lies in the interval:

The correct option is A $(0, \frac{1}{2})$
$90^{\circ} < θ < 180^{\circ} \Rightarrow a . b < 0 \Rightarrow (2 x^{2}^i + 4 x^j +^k) . (7^i - 2^j + x^k) < 0 \Rightarrow 14 x^{2} - 8 x + x < 0 \Rightarrow 14 x^{2} - 7 x < 0 \Rightarrow 7 x (2 x - 1) < 0 \Rightarrow 0 < x < \frac{1}{2}$