If the angle between the vectors 2 α2 hat i +4 α hat j + hat k and 7 hat i -2 hat j +α hat k is obtuse, then

Question

If the angle between the vectors 2 α2 hat i +4 α hat j + hat k and 7 hat i -2 hat j +α hat k is obtuse, then (A) α>(1/2) (B) 0<α<(1/2) (C) α<0 (D) |α|<(1/ text ? )

Tardigrade Admin · Accepted Answer

Given vectors 2 α2 hat i +4 α hat j + hat k text and 7 hat i -2 hat j +α hat k Angle between these vector are obtuse ∴ cos θ<0 ((2 α2 hat i +4 α hat j + hat k )(7 hat i -2 hat j +α hat k )/|2 α2 hat i +4 α hat j + hat k ||7 hat i -2 hat j +α hat k |) ⇒ 14 α2-8 α+α<0 ⇒ 14 α2-7 α<0 ⇒ 7 α(2 α-1) < 0 ⇒ α ∈(0, (1/2)) ∴ 0 < α < (1/2)

Q. If the angle between the vectors
$2 α^{2} \hat{i} + 4 α \hat{j} + \hat{k}$ and $7 \hat{i} - 2 \hat{j} + α \hat{k}$ is obtuse, then

$α > \frac{1}{2}$

$0 < α < \frac{1}{2}$

$α < 0$

$∣ α ∣ < \frac{1}{?}$

Q. If the angle between the vectors 2α2i^+4αj^​+k^ and 7i^−2j^​+αk^ is obtuse, then

α>21​

0<α<21​

α<0

∣α∣< ? 1​

Given vectors 2α2i^+4αj^​+k^ and 7i^−2j^​+αk^ Angle between these vector are obtuse ∴cosθ<0 ∣2α2i^+4αj^​+k^∣∣7i^−2j^​+αk^∣(2α2i^+4αj^​+k^)(7i^−2j^​+αk^)​ ⇒14α2−8α+α<0⇒14α2−7α<0 ⇒7α(2α−1)<0⇒α∈(0,21​) ∴0<α<21​

Q. If the angle between the vectors
$2 α^{2} \hat{i} + 4 α \hat{j} + \hat{k}$ and $7 \hat{i} - 2 \hat{j} + α \hat{k}$ is obtuse, then

$α > \frac{1}{2}$

$0 < α < \frac{1}{2}$

$α < 0$

$∣ α ∣ < \frac{1}{?}$