Scalar Triple...

Scalar Triple Product

Trending Questions

If 5^x-3×3^2x-8= 225

Then, x=?

$\to V = 2^i +^j -^k$ 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

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

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If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, then $(\to a + \to b + \to c) \cdot [(\to a + \to b) \times (\to a + \to c)]$ equals

0
$2. [\to a \to b \to c]$
$- [\to a \to b \to c]$
$[\to a \to b \to c]$

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If p(x)=x²-2√2x+1then find p(2√2)

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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

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

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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

$\pm \sqrt{7}$
$N o n e o f t h e s e$
$\pm \sqrt{5}$
$\pm \sqrt{6}$

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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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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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Let $\to a = a_{1}^i + α_{2}^j + a_{3}^k, \to b = b_{1}^i + b_{2}^j + b_{3}^k a n d \to c = c_{1}^i + c_{2}^j + c_{3}^k$ be three non-zero vectors such that $\to c$ is a unit vector perpendicular to both the vectors $\to a$ and $\to b$ . If the angle between $\to a$ and $\to b$ is $\frac{π}{6},$
then ${∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣}^{2}$ is equal to

0
1
$\frac{1}{4} (a_{1}^{2} + a_{2}^{2} + a_{3}^{2}) (b_{1}^{2} + b_{2}^{2} + b_{3}^{2})$
$\frac{3}{4} (a_{1}^{2} + a_{2}^{2} + a_{3}^{2}) (b_{1}^{2} + b_{2}^{2} + b_{3}^{2}) (c_{1}^{2} + c_{2}^{2} + c_{3}^{2})$

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Q. Let

\to a =^i -^j, \to b = \to j -^k, \to c =^k -^i . I f \to d

is a unit vector such that

\to a . \to d = 0 = [\to b \to c \to d],

then

\to d

equals

$\pm \frac{^i +^j -^k}{\sqrt{3}}$
$\pm \frac{^i +^j - 2^k}{\sqrt{6}}$
$\pm \frac{^i +^j +^k}{\sqrt{3}}$
$\pm^k$

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Q. The value of

[\to a - \to b \to b - \to c \to c - \to a]

where

| \to a | = 1, | \to b | = 5, | \to c | = 3

, is

0
1
6
None of these

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Q. If scalar triple product of vectors

^i +^j +^k, 3^i + 4^j + 5^k, 7^i + 2^j + 11^k

is given by the determinant

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

then

a_{1} + b_{2} + c_{3} =

__.

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[\to a, \to b, \to c] \neq [\to b, \to c, \to a] \neq [\to c, \to a, \to b]

True
False

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If $\to a, \to b, \to c$ , and $\to d,$ are the unit vectors such that $(\to a \times \to b) . (\to c \times \to d) = 1$ and $\to a . \to c = \frac{1}{2},$ then

$\to a, \to b, \to d$ are non-coplanar
$\to b, \to d$ are non-parallel
$\to a, \to d$ are parallel and
$\to b, \to c$ are parallel
$\to a, \to b, \to c$ are non-coplanar

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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. {X⁴(x-1)1}÷x²+x+1is greater than 0 .find the exhaustive values of x

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Q. If the sun of the toys of the equation x^2-px+q=0 be m times their difference, prove that p^2(m^2-1)=4m^2q

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(\to a \times \to b) . \to c = \to a (\to b \times \to c)

True
False

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Q. Let

\to a =^i -^j, \to b = \to j -^k, \to c =^k -^i . I f \to d

is a unit vector such that

\to a . \to d = 0 = [\to b \to c \to d],

then

\to d

equals

$\pm \frac{^i +^j -^k}{\sqrt{3}}$
$\pm \frac{^i +^j - 2^k}{\sqrt{6}}$
$\pm \frac{^i +^j +^k}{\sqrt{3}}$
$\pm^k$

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The volume of tetrahedron whose vertices are

A = (3, 2, 1) , ~B = (1, 2, 4), ~ C = (4, 0, 3), ~ D = (1, 1, 7)~will be $- --- -$ cubic units

5
None of the above

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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

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

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Q. Value of scalar triple product is zero if any 2 vectors are identical.

True
False

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