Scalar Triple...

Scalar Triple Product

Trending Questions

Q. If

x

is parallel to

y

and

z

where

x = 2^i +^j + α^k, y = α^i +^k

and

z = 5^i -^j,

then

α

is equal to

$\pm \sqrt{5}$
$\pm \sqrt{6}$
$\pm \sqrt{7}$
None of these

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Q. Two perpendicular unit vectors

\to a

and

\to b

are such that

[\to r \to a \to b] = \frac{5}{4},

\to r \cdot (3 \to a + 2 \to b) = 0

and

\frac{- 4}{3} \to r . \to b \int - 2 \to r . \to a \frac{x + 1}{x^{2} + 1} d x = \frac{π}{2}

. Then which of the following is(are) correct ?

$| \to r |^{2} = \frac{19}{8}$
$| \to r |^{2} = \frac{7}{4}$
$\to r = \frac{\to a}{2} - \frac{3 \to b}{4} + \frac{5}{4} (\to a \times \to b)$
$\to r = - \frac{\to a}{2} + \frac{3 \to b}{2} + \frac{5}{4} (\to a \times \to b)$

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21 x^{2} - 28 x + 10 = 0

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17 x^{2} + 28 x + 12 = 0

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The volume of parallelopipped formed by following 3 vectors will be___cubic units.

$\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

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Q. If the vector a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle between b and c is

\frac{2 π}{3}

then |[a b c ]| =

24
12
$12 \sqrt{3}$
$24 \sqrt{3}$

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$\to V = 2^i +^j -^k$ and $\to W =^i + 3^k$ . If $\to U$ is a unit vector, then the maximum value of the scalar triple product $[\to U \to V \to W]$ is

-1
$\sqrt{10} + \sqrt{6}$
$\sqrt{59}$
$\sqrt{60}$

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If $\to a, \to b, \to c$ are non-coplanar vectors and $\to d = λ \to a + μ \to b + ν \to c,$ then $λ$ equal to

$\frac{[\to d \to b \to c]}{[\to b \to a \to c]}$
$\frac{[\to b \to c \to d]}{[\to b \to c \to a]}$
$\frac{[\to b \to d \to c]}{[\to a \to b \to c]}$
$\frac{[\to c \to b \to d]}{[\to a \to b \to c]}$

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Q. The value of

∣ ∣ ∣ \begin{matrix} 2 & 4 - 1 & 2 \end{matrix} ∣ ∣ ∣

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if z₁= 7-3i, z₂= 3 + root3 i , z₃=4-8i, then find z₁z₂z₃.

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