If a is a non-zero vector- then the value of - a-a-k-a-k- is

Let a=a_xî +a_yĵ+a_zk̂ nbsp; ⇒î× (a×î)= ((î·î)a (î·a)î) = (a (a·î)i)=a a_xî Similarly, ⇒ĵ× (a×ĵ)= a a_yĵ Similarly, ⇒k̂× (a×k̂)= a a_zk̂ Adding all above thre ...

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Standard XII

Mathematics

Linear Combination of Vectors

If a is a non...

Question

If $\to a$ is a non-zero vector, then the value of $^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k)$ is

3 \to a

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2 \to a

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\to a

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\to 0

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Solution

The correct option is B $2 \to a$
Let $\to a = a_{x}^i + a_{y}^j + a_{z}^k$
$\Rightarrow^i \times (\to a \times^i) = ((^i \cdot^i) \to a - (^i \cdot \to a)^i)$
$= (\to a - (\to a \cdot^i) ¯ i) = \to a - a_{x}^i$
Similarly,
$\Rightarrow^j \times (\to a \times^j) = \to a - a_{y}^j$
Similarly,
$\Rightarrow^k \times (\to a \times^k) = \to a - a_{z}^k$
Adding all above three cases, we get
$=^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k) = 3 \to a - (a_{x}^i + a_{y}^j + a_{z}^k)$
$= 3 \to a - \to a = 2 \to a$

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Linear Combination of Vectors

Standard XII Mathematics

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If →a is a non-zero vector, then the value of ^i×(→a×^i)+^j×(→a×^j)+^k×(→a×^k) is

If $\to a$ is a non-zero vector, then the value of $^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k)$ is