If a and b are two non-collinear vectors such that - a - -3- b - -4 and a-b- -2- -3k- then the value of -a-b- - a - - b - 2 is equal to

The correct option is C 7 72 We know that { |a b| #160;| a | | b | #160; #160;} #160;^ 2 =| a b | #160;^ 2 | a | #160;^ 2 | b | #16 ...

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Standard XII

Mathematics

Algebra of Limits

If a and ...

Question

If $a$ and $b$ are two non-collinear vectors such that $| a | = 3, | b | = 4$ and $a - b =^i + 2^j + 3^k$ , then the value of ${\frac{| a - b |}{| a | | b |}}^{2}$ is equal to

\frac{1}{24}

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\frac{5}{72}

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\frac{7}{72}

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\frac{7}{48}

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Solution

The correct option is C $\frac{7}{72}$
We know that
${\frac{| a - b |}{| a | | b |}}^{2} = \frac{{| a - b |}^{2}}{{| a |}^{2} {| b |}^{2}} = \frac{1 + 4 + 9}{9 \times 16} = \frac{7}{72}$

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Similar questions

Q. If

\vec{a} and \vec{b}

are two non-zero non-collinear vectors such that

|\vec{a} \times \vec{b}| = 1 and |\vec{a} . \vec{b}| = \sqrt{3}

, then the angle between

\vec{a} and \vec{b}

is _____________.

Find the value of $λ$ such that the vectors $\to a = 2^i + λ^j +^k a n d \to b =^i + 2^j + 3^k$ are orthogonal.

(a) 0

(b) 1

(d) $\frac{- 5}{2}$

Q. Let

\to a = -^i -^k,^b = -^i +^j

and

\to c =^i + 2^j + 3^k

be three given vectors. If

\to r

is a vector such that

\to r \times \to b = \to c \times \to b

and

\to r \cdot \to a = 0,

then the value of

\to r \cdot \to b =

Q. Let

\to a, \to b, \to c

are three non zero vectors such that any two of them are non-collinear. If

\to a + \to b

is collinear with

\to c

and

\to b + \to c

is collinear with

\to a

, then the value of

\to a + \to b + \to c

equals

Q. Let

\to c

be a vector perpendicular to the vectors

\to a =^i +^j -^k

and

\to b =^i + 2^j +^k .

\to c \cdot (^i +^j + 3^k),

then the value of

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If a and b are two non-collinear vectors such that |a|=3,|b|=4 and a−b=^i+2^j+3^k, then the value of {|a−b||a||b|}2 is equal to

The correct option is C 772We know that{|a−b||a||b|}2=|a−b|2|a|2|b|2=1+4+99×16=772

If $a$ and $b$ are two non-collinear vectors such that $| a | = 3, | b | = 4$ and $a - b =^i + 2^j + 3^k$ , then the value of ${\frac{| a - b |}{| a | | b |}}^{2}$ is equal to

The correct option is C $\frac{7}{72}$
We know that
${\frac{| a - b |}{| a | | b |}}^{2} = \frac{{| a - b |}^{2}}{{| a |}^{2} {| b |}^{2}} = \frac{1 + 4 + 9}{9 \times 16} = \frac{7}{72}$