For any vector x- the value of x-2-x-2-x-k-2 is equal toA- -x-2B- 2- x -2- 3- x -2D- 4- x -2

The correct option is B 2|x |^2Let x makes an angle of a,b,c with î ,ĵ,k̂ respectively. ⇒(x×î)^2+(x×ĵ)^2+(x×k̂)^2 =|x |^2 (sin^2 a+sin^2b+sin^2c ) =2|x | ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

For any vecto...

Question

For any vector $\to x$ , the value of $(\to x \times^i)^{2} + (\to x \times^j)^{2} + (\to x \times^k)^{2}$ is equal to

| \to x |^{2}

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2 | \to x |^{2}

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3 | \to x |^{2}

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4 | \to x |^{2}

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Solution

The correct option is B $2 | \to x |^{2}$
Let $\to x$ makes an angle of $a, b, c$ with $^i,^j,^k$ respectively.
$\Rightarrow (\to x \times^i)^{2} + (\to x \times^j)^{2} + (\to x \times^k)^{2} = | \to x |^{2} ({sin}^{2} a + {sin}^{2} b + {sin}^{2} c) = 2 | \to x |^{2}$

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Similar questions

Q. For any vector

\to x

, the value of

| \to x \times^i |^{2} + | \to x \times^j |^{2} + | \to x \times^k |^{2}

is equal to

Q. If

ˆ a

is a unit vector and projection of

\to x

along

ˆ a

2

units and

(ˆ a \times \to x) + \to b = \to x

, then

\to x

is equal to

Q. If a is a unit vector such that

(\to x - \to a)

(\to x + \to a) = 3

. Find

(x)

Q. Vector

\to x

is Vectors

\to x, \to y

and

\to z,

each of magnitude

\sqrt{2},

make an angle of

60^{\circ}

with each other.

\to x \times (\to y \times \to z) = \to a, \to y \times (\to z \times \to x) = \to b

and

\to x \times \to y = \to c .

Q. If

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and

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For any vector →x, the value of (→x×^i)2+(→x×^j)2+(→x×^k)2 is equal to

The correct option is B 2|→x|2Let →x makes an angle of a,b,c with ^i,^j,^k respectively. ⇒(→x×^i)2+(→x×^j)2+(→x×^k)2 =|→x|2(sin2a+sin2b+sin2c) =2|→x|2

For any vector $\to x$ , the value of $(\to x \times^i)^{2} + (\to x \times^j)^{2} + (\to x \times^k)^{2}$ is equal to

The correct option is B $2 | \to x |^{2}$
Let $\to x$ makes an angle of $a, b, c$ with $^i,^j,^k$ respectively.
$\Rightarrow (\to x \times^i)^{2} + (\to x \times^j)^{2} + (\to x \times^k)^{2} = | \to x |^{2} ({sin}^{2} a + {sin}^{2} b + {sin}^{2} c) = 2 | \to x |^{2}$