If a-k- and b- then the vectors- a-a-a-k-k-b- - -b-b-k-k- and -2k- are

The correct option is A Mutually PerpendicularSolving #160; (a·i)i+(a·j)j+(a·k)k=a (b·i)i+(b·j)j+(b·k)k=b a·b=0 a·(i+j 2k)=0 b·(i+j 2 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗=î+ĵ+k...

Question

If $\to a =^i +^j +^k$ and $\to b =^i -^j$ , then the vectors, $(\to a .^i)^i + (\to a .^j)^j + (\to a .^k)^k, (\to b .^i)^i + (\to b .^j)^j + (\to b .^k)^k$ and $^i +^j - 2^k$ are

Mutually Perpendicular

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Coplanar

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Forms a Parallelopiped of volume2 units

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Forms a Parallelopiped of volume 3 units

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Solution

The correct option is A Mutually Perpendicular
Solving
$(¯ ¯ ¯ a \cdot ¯ i) ¯ i + (¯ ¯ ¯ a \cdot ¯ j) ¯ j + (¯ ¯ ¯ a \cdot ¯ ¯ ¯ k) ¯ ¯ ¯ k = ¯ ¯ ¯ a$
$(¯ ¯ b \cdot ¯ i) ¯ i + (¯ ¯ b \cdot ¯ j) ¯ j + (¯ ¯ b \cdot ¯ ¯ ¯ k) ¯ ¯ ¯ k = ¯ ¯ b$
$¯ ¯ ¯ a \cdot ¯ ¯ b = 0$
$¯ ¯ ¯ a \cdot (¯ i + ¯ j - 2 ¯ ¯ ¯ k) = 0$
$¯ ¯ b \cdot (¯ i + ¯ j - 2 ¯ ¯ ¯ k) = 0$
So, $¯ ¯ ¯ a, ¯ ¯ b$ & $¯ i + ¯ j - 2 ¯ ¯ ¯ k$ are mutually $⊥$ .

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Similar questions

Q. If

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

and

\to c^{'} = 2^i +^j -^k

. Then altitude of the parallelopiped formed by the vectors

\to a, \to b, \to c

having base formed by

\to b

and

\to c

(\to a, \to b, \to c

and

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

are reciprocal system of vectors)

Q. Find the altitude of a parallelopiped determined by

\to a, \to b, \to c

if yhe base

\to a, & \to b

and if

\to a =^i +^j +^k; \to b = 2^i + 4^j -^k & \to c =^i +^j + 3^k

Q. If

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

and

\to c^{'} = 2^i +^j -^k

. Then altitude of the parallelopiped formed by the vectors

\to a, \to b, \to c

having base formed by

\to b

and

\to c

(\to a, \to b, \to c

and

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

are reciprocal system of vectors)

Q. If

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

and

\to c^{'} = 2^i +^j -^k

. Then altitude of the parallelopiped formed by the vectors

\to a, \to b, \to c

having base formed by

\to b

and

\to c

(\to a, \to b, \to c

and

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

are reciprocal system of vectors)

Q. If

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

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

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

and

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

, then

(\to a \times \to b) \times (\to c \times \to d)

is a vector orthogonal to both

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If →a=^i+^j+^k and →b=^i−^j, then the vectors, (→a.^i)^i+(→a.^j)^j+(→a.^k)^k,(→b.^i)^i+(→b.^j)^j+(→b.^k)^k and ^i+^j−2^k are

If $\to a =^i +^j +^k$ and $\to b =^i -^j$ , then the vectors, $(\to a .^i)^i + (\to a .^j)^j + (\to a .^k)^k, (\to b .^i)^i + (\to b .^j)^j + (\to b .^k)^k$ and $^i +^j - 2^k$ are