Find the value of m such that the vector 4-2-2k- is orthogonal to the vector -2-mk-

We know that if two vectors are orthogonal, their scalar product is zero. nbsp; So, we have nbsp; Let say A=4î 2ĵ 2k̂ and B= î+2ĵ mk̂ Since, its scalar prod ...

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Standard XI

Physics

Multiplication with Vectors

Find the valu...

Question

Find the value of $m$ such that the vector $4^i - 2^j - 2^k$ is orthogonal to the vector $-^i + 2^j - m^k$

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Solution

The correct option is A $4$
We know that if two vectors are orthogonal, their scalar product is zero.
So, we have
Let say $\to A = 4^i - 2^j - 2^k$ and $\to B = -^i + 2^j - m^k$
Since, its scalar product will be zero
$\Rightarrow \to A . \to B = 0$
$\Rightarrow (4^i - 2^j - 2^k) . (-^i + 2^j - m^k) = 0$
$\Rightarrow - 4 - 4 + 2 m = 0 \Rightarrow m = 4$

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Find the value of m such that the vector 4^i−2^j−2^k is orthogonal to the vector −^i+2^j−m^k

The correct option is A 4We know that if two vectors are orthogonal, their scalar product is zero. So, we have Let say →A=4^i−2^j−2^k and →B=−^i+2^j−m^k Since, its scalar product will be zero ⇒ →A.→B=0 ⇒ (4^i−2^j−2^k).(−^i+2^j−m^k)=0 ⇒ −4−4+2m=0⇒ m=4

Find the value of $m$ such that the vector $4^i - 2^j - 2^k$ is orthogonal to the vector $-^i + 2^j - m^k$