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1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are scalars. Show that a = 2i + 3j+ k, b=i- j and c = 7i+ 3j+ 2k are coplanar by writing a as a linear combination of b and c.

1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are scalars. Show that a = 2i + 3j+ k, b=i- j and c = 7i+ 3j+ 2k are coplanar by writing a as a linear combination of b and c.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are scalars. Show that a = 2i +3j + k, b = i- j and c = 7i+ 3j+ 2k are coplanar by writing a as a linear combination of b and c. 2) Eliminate the parameter t to find the rectangular equation of the curve represented by the parametric equations x =√ and y=√1 And sketch the curve (indicate the direction of trace in increasing order of t). 3) Find a unit vector that is perpendicular to the plane containing the vectors a = (2, -6, -3) and b = (4, 3, -1) without using cross product.
Transcribed Image Text:1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are scalars. Show that a = 2i +3j + k, b = i- j and c = 7i+ 3j+ 2k are coplanar by writing a as a linear combination of b and c. 2) Eliminate the parameter t to find the rectangular equation of the curve represented by the parametric equations x =√ and y=√1 And sketch the curve (indicate the direction of trace in increasing order of t). 3) Find a unit vector that is perpendicular to the plane containing the vectors a = (2, -6, -3) and b = (4, 3, -1) without using cross product.
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