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Chapter 3: Q4P (page 112)

In Problems 1 to 5, all lines are in the (x,y) plane.

4. Write, in parametric form, the equation of the straight line that is perpendicular to r=(2i+4j)+(i-2j)tand goes through (1,0).

Short Answer

Expert verified

The parametric form of the equation is r=i+(2i+j)t.

Step by step solution

01

Concept of slop of the line

Slope of the line of the form ai+bjism=ba .

Product of slopes of two perpendicular lines is m1m2=-1.

02

Determine the parametric form

The equation of line is r=(2i+4j)+(i-2j)t and passing through(1,0).

Let L=(i-2j).

The slope of line L is m=-21=-2.

Then the slope of line perpendicular to L is -1m=12.

Then the equation of line perpendicular to L is L1=(2i+j).

The line passing through (1,0) and parallel to L1=(2i+j) is,

12=y-0x-1 鈭�y-y1x-x1=m

x-12=y

.

Hence, the parametric form of the equation is r=i+(2i+j)t.

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Most popular questions from this chapter

Verify that each of the following matrices is Hermitian. Find its eigenvalues and eigenvectors, write a unitary matrix U which diagonalizes H by a similarity transformation, and show thatU-1HU is the diagonal matrix of eigenvalues.

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Verify (6.14) by multiplying the matrices and using trigonometric addition formulas.

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(a) If Cis orthogonal and Mis symmetric, show that C-1MCis symmetric.

(b) IfC is orthogonal and Mantisymmetric, show thatC-1MCis antisymmetric.
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