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Question
Let →U=2^i+^j−^k,−→W=^i+3^k, if →V is a unit vector,then the maximum value of [→U,→V,−→W] is
Let →U=2^i+^j−^k,−→W=^i+3^k, if →V is a unit vector,then the maximum value of [→U,→V,−→W] is
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Solution
The correct option is C √59
[→U,→V,−→W]=→U.(→V×−→W)
=∣∣∣→U∣∣∣∣∣∣→V×−→W∣∣∣
=→U×−→W from the question.
=⎡⎢⎣^i^j^k21−1103⎤⎥⎦
=^i(3−0)−^j(6+1)+^k(0−1)
=3^i−7^j−^k
∴∣∣∣→V×−→W∣∣∣=√32+72+1=√59
∣∣∣→U∣∣∣=1(given)
⇒[→U,→V,−→W]≤√59
[→U,→V,−→W]=→U.(→V×−→W)
=∣∣∣→U∣∣∣∣∣∣→V×−→W∣∣∣
=→U×−→W from the question.
=⎡⎢⎣^i^j^k21−1103⎤⎥⎦
=^i(3−0)−^j(6+1)+^k(0−1)
=3^i−7^j−^k
∴∣∣∣→V×−→W∣∣∣=√32+72+1=√59
∣∣∣→U∣∣∣=1(given)
⇒[→U,→V,−→W]≤√59
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