Given: p || q, and r || s.
2 answers:
Answer:
A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
Step-by-step explanation:
In the figure attached, a plot of the problem is shown.
Given p || q and r is a transversal which cut p and q, then ∠1 ≅ ∠5 and ∠2 ≅ ∠6.
Given r || s and q is a transversal which cut r and s, then ∠6 ≅ ∠14 and ∠8 ≅ ∠16.
From the picture we see that ∠1 and ∠2 are supplementary, that is, their addition is equal to 180º. ∠2 ≅ ∠6 and ∠6 ≅ ∠14, then ∠2 ≅ ∠14, in consequence ∠1 and ∠14 are supplementary.
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Answer:
a)
b)
c)
Step-by-step explanation:
a) Let <u>a</u>=<2,1,-3>
The magnitude of <u>a</u> is
The unit vector in the direction of a is
Using the relation , we have
b) Let a=2i - 3j + 4k
Using the relation , we have
c) Let us first find the sum of <1, 2, -3> and <2, 4, 1> to get:
<1+2, 2+4, -3+1>=<3, 6, -2>
Let a=<3, 6, -2>
The magnitude is
The unit vector in the direction of <u>a</u> is
Using the relation , we have