If -k- -k- and 2-3-mk- are coplanar- then find m

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Standard XII

Mathematics

Test for Collinearity of Vectors

If î+ĵ+k̂, ...

Question

If $^i +^j +^k,^i -^j +^k$ and $2^i + 3^j + m^k$ are coplanar, then find $m$

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Solution

If two vectors are co planar, then any vector can be expressed as linear combination of other two vector
then,
$2^i + 3^j + m^k = a (^i +^j +^k) + b (^i -^j +^k)$
Comparing coefficient of $^i$ ,
$2 = a + b$
Comparing coefficient of $^k$ ,
$m = a + b$
Therefore
$m = a + b = 2$
So, $m = 2$

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If ^i+^j+^k, ^i−^j+^k and 2^i+3^j+m^k are coplanar, then find m

If two vectors are co planar, then any vector can be expressed as linear combination of other two vectorthen,2^i+3^j+m^k=a(^i+^j+^k)+b(^i−^j+^k)Comparing coefficient of ^i,2=a+bComparing coefficient of ^k,m=a+bTherefore m=a+b=2So, m=2

If $^i +^j +^k,^i -^j +^k$ and $2^i + 3^j + m^k$ are coplanar, then find $m$

If two vectors are co planar, then any vector can be expressed as linear combination of other two vector
then,
$2^i + 3^j + m^k = a (^i +^j +^k) + b (^i -^j +^k)$
Comparing coefficient of $^i$ ,
$2 = a + b$
Comparing coefficient of $^k$ ,
$m = a + b$
Therefore
$m = a + b = 2$
So, $m = 2$