+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Vector Algebra

Question
CBSEENMA12034206
Wired Faculty App

Use vector method only to find the values of a and b if points (2, b, 3), (a, – 5, 1) and ( – 1, 11, 9) are collinear.

Solution
Let A (2, b, 3), B (a. – 5, 1) and C (– 1, 11, 9) be given points.
AB with rightwards arrow on top space equals space straight P. straight V. space of space straight B space minus space straight P. straight V. space of space straight A space equals space open parentheses straight a space straight i with hat on top space minus space 5 space straight j with hat on top space plus space straight k with hat on top close parentheses space minus space left parenthesis 2 space straight i with hat on top space plus space straight b space straight j with hat on top plus space 3 space straight k with hat on top right parenthesis space space space space space space equals space left parenthesis straight a minus 2 right parenthesis space straight i with hat on top space minus space left parenthesis straight b plus 5 right parenthesis space straight j with hat on top space space minus space 2 space straight k with hat on top AC with rightwards arrow on top space equals space straight P. straight V. space of space straight C space minus space straight P. straight V. space of space straight A space equals space open parentheses negative straight i with hat on top space plus 11 stack straight j space with hat on top plus 9 space straight k with hat on top close parentheses space minus space left parenthesis 2 space straight i with hat on top space plus space straight b space straight j with hat on top space plus space 3 space straight k with hat on top right parenthesis space space space space space space space equals negative 3 straight i with hat on top space plus space left parenthesis 11 minus straight b right parenthesis space straight j with hat on top space plus space 6 space straight k with hat on top
Since A, B, C are collinear
therefore space space space open vertical bar AB with rightwards arrow on top space cross times space AC with rightwards arrow on top space close vertical bar space equals space 0 with rightwards arrow on top therefore space space space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row cell straight a minus 2 end cell cell negative straight b minus 5 end cell cell negative 2 end cell row cell negative 3 end cell cell 11 minus straight b end cell 6 end table close vertical bar space equals space 0 with rightwards arrow on top rightwards double arrow space space space space open vertical bar table row cell negative straight b minus 5 end cell cell space minus 2 end cell row cell 11 minus straight b end cell cell space space space 6 end cell end table close vertical bar space straight i with hat on top space minus space open vertical bar table row cell straight a minus 2 end cell cell space minus 2 end cell row cell negative 3 end cell cell space space space 6 end cell end table close vertical bar straight j with hat on top space plus space open vertical bar table row cell straight a minus 2 space space space end cell cell negative straight b minus 5 end cell row cell negative 3 end cell cell space 11 minus straight b end cell end table close vertical bar straight k with hat on top space equals 0 with rightwards arrow on top therefore space space space space space left parenthesis negative 6 straight b minus 30 space plus 22 space minus 2 straight b right parenthesis straight i with hat on top space minus space left parenthesis 6 straight a minus 12 minus 6 right parenthesis space straight j with hat on top space plus space open square brackets left parenthesis straight a minus 2 right parenthesis thin space left parenthesis 1 minus straight b right parenthesis space plus 3 space left parenthesis straight b minus 5 right parenthesis close square brackets straight k with hat on top space equals space 0 therefore space space space space minus 6 straight b minus 30 plus 22 minus 2 straight b space equals space 0 comma space space space space 6 straight a minus 12 minus 6 space equals space 0 therefore space space space space space minus 8 straight b space equals space 8 comma space space space 6 straight a space equals 18 rightwards double arrow space space space space space space straight b space equals space minus 1 comma space space space straight a space equals space 3 space space space space space rightwards double arrow space space space space straight a space equals space 3 comma space space space straight b space equals space minus 1

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s2

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation