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Graph of Quadratic Expression

If a⃗ = pi⃗...

Question

If $\to a = p \to i + 3 \to j - 7 \to k, \to b = p \to i - p \to j + 4 \to k$ and if the angle between $a$ and $b$ is acute, then the values of $p$ lies in

A

p < - 4

or

p > 7

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B

(- 7, 4)

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C

p \leq - 4

and

p \geq 7

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D

[- 7, 4]

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Solution

The correct option is A $p < - 4$ or $p > 7$

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Similar questions

P = \to A + \to B

Q = \to A - \to B

if magnitude of

P

Q

are equal then angle between

A

B

θ

is an acute angle and

s i n θ = \frac{p - 6}{8 - p},

then p must satisfy

\to a = 3 \to i + p \to j + 3 \to k

\to b = 2 \to i + 3 \to j + q \to k

are parallel vectors if

p = \frac{9}{2}

q = 2

\to a = a_{1} \to i + a_{2} \to j + a_{3} \to k

\to b = b_{1} \to i + b_{2} \to j + b_{3} \to k

are parallel, then

\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}}

Q. If P and Q are the points of trisection of the line joining A(2, -2) and B(-7, 4) such that P is nearer to A, then the coordinates of P and Q are:

cos P = 1_{/ 7}

cos Q = 13_{/ 14}

, where P and Q both are acute angles. Then, the value of

P - Q

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