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If a is a non-zero real number, then pro...

If a is a non-zero real number, then prove that the vectors ` vecalpha=a hat i+2a hat j-3a hat k , vecbeta=(2a+1) hat i+(2a+3) hat j+(a+1) hat ka n d , vecgamma=(3a+5) hat i+(a+5) hat j+(a+2) hat k` are never coplanar.

A

{0}

B

`(0, infty)`

C

`(-infty, 1)`

D

`(1, infty)`

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A
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Find the values of a for which are vectors vecalpha= hat i+2 hat j+ hat k , vecbeta=a hat i+ hat j+2 hat k\ a n d\ vecgamma= hat i+2 hat j+a hat k are coplanar. \

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the angle between the vectors 2hat i-3hat j+2hat k and hat i+5hat j+5hat k is

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The value of p so that vectors 2hat i-hat j+hat k , hat i+2hat j-3hat k and 3hat i+phat j+5hat k are coplanar is

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