Find the value of m such that the vector 6-8-2k- is orthogonal to the vector -3-mk-

We know that if two vectors are orthogonal, their scalar product is zero. nbsp; So, we have nbsp; Let say A=6î 8ĵ 2k̂ and B= 3î+ĵ mk̂ Since, its scalar p ...

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Standard XIII

Physics

Projection of Vectors

Find the valu...

Question

Find the value of $m$ such that the vector $6^i - 8^j - 2^k$ is orthogonal to the vector $- 3^i +^j - m^k$

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Solution

We know that if two vectors are orthogonal, their scalar product is zero.

So, we have

Let say $\to A = 6^i - 8^j - 2^k$ and $\to B = - 3^i +^j - m^k$

Since, its scalar product will be zero, $\to A . \to B = 0$

$\Rightarrow (6^i - 8^j - 2^k) . (- 3^i +^j - m^k) = 0$

$\Rightarrow - 18 - 8 + 2 m = 0 \Rightarrow m = 13$

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Find the value of m such that the vector 6^i−8^j−2^k is orthogonal to the vector −3^i+^j−m^k

We know that if two vectors are orthogonal, their scalar product is zero. So, we have Let say →A=6^i−8^j−2^k and →B=−3^i+^j−m^k Since, its scalar product will be zero, →A.→B=0 ⇒ (6^i−8^j−2^k).(−3^i+^j−m^k)=0 ⇒ −18−8+2m=0⇒ m=13

Find the value of $m$ such that the vector $6^i - 8^j - 2^k$ is orthogonal to the vector $- 3^i +^j - m^k$