Hello, i've got this assignment from my Algebra teacher, although i don't have a clue how to do that, can someone help me?(don't have the answers)
For each question, mark T for true or F for False:
(a) For Vectors U,V and W as Rn , if u+w=v+w so u=v?
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(b) For vectors U,V and W as Rn, if u.w=v.w so u=v?
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(c) For vectors U,V and W in R³, if u is orthogonal v, and v is orthogonal by w, so u is orthogonal by w?
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(d) In R³ space, if a line is paralel to a plane, so a director vector of this line is paralel to the normal vector of the plane?
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(e) In R³ space, if a line is perpendicular to a plane, so director vector of this line is paralel to the normal vector of the plane?
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(f) In R³ space, if two planes are not paralel so they have to intercept in a line?
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(g) In R³ space, if two lines are not paralel, so they have to intercept in some point?
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(h) The angular measure between a non-zero vector and itself is zero (degrees or radians) ?
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(i) The angular measure between two non-zero and orthogonal vectors is a right angle (with measurements in radians)
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(j) There are no u and v such that ang (u, v) = arcsen (-1/2)
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For each question, mark T for true or F for False:
(a) For Vectors U,V and W as Rn , if u+w=v+w so u=v?
( )
(b) For vectors U,V and W as Rn, if u.w=v.w so u=v?
( )
(c) For vectors U,V and W in R³, if u is orthogonal v, and v is orthogonal by w, so u is orthogonal by w?
( )
(d) In R³ space, if a line is paralel to a plane, so a director vector of this line is paralel to the normal vector of the plane?
( )
(e) In R³ space, if a line is perpendicular to a plane, so director vector of this line is paralel to the normal vector of the plane?
( )
(f) In R³ space, if two planes are not paralel so they have to intercept in a line?
( )
(g) In R³ space, if two lines are not paralel, so they have to intercept in some point?
( )
(h) The angular measure between a non-zero vector and itself is zero (degrees or radians) ?
( )
(i) The angular measure between two non-zero and orthogonal vectors is a right angle (with measurements in radians)
( )
(j) There are no u and v such that ang (u, v) = arcsen (-1/2)
( )