Find the value of `lambda` , if four points with position vectors `3 hati + 6 hatj + 9 hatk, hati + 2 hatj + 3 hatk, 2 hati + 3 hatj + hatk and 4 hati + 6 hatj + lambdahat k` are coplanar.

Find the value of `lambda` , if four points with position vectors `3 h

1.	Find the value of `lambda` , if four points with position vectors `3 hati + 6 hatj + 9 hatk, hati + 2 hatj + 3 hatk, 2 hati + 3 hatj + hatk and 4 hati + 6 hatj + lambdahat k` are coplanar.
Answer» `AB=(-2,-4,-6)`, .`AC=(-1,-3,-8)` `AD=(1,0,lambda-9)` As, all these vectors are coplanar, So`\|(-2,-4,-6), (-1.-3,-8),(1,0,lambda-9)\|=0`Hence,`Lambda=2`

Discussion

No Comment Found

Related InterviewSolutions

Describe how the following changes are brought about: (i)Pig iron into steel. (ii)Zinc oxide into metallic zinc. (iii)Impure titanium into pure titanium.
(a) Give an example of zone refining of metals. (b) What is the role of cryolite in the metallurgy of aluminium?
Write two differences between multimolecular colloids and macromolecular colloids ?
(a) What is "population" according to you as a biology student ? (b) "The size of a population for any species is not a static parameter." Justify the statement with specific reference to fluctuations in the population density of a region in a given periods of time. OR (a ) What is hydrarch succession ? (b) Compare the pioneer species and climax communities of hydrarch and xerarch succession respectively. (c) List the factors upon which the type of invading pioneer species depend in secondary hydrarch succession. Why is the rate of this succession faster than that of primary succession ?
It is often said that the pyramid of energy is always upright. On the other hand, the pyramid of biomass can be both upright and inverted." Explain with the help of example and sketches .
List the different attributes that a population has and not an individual organism. ( b) What is population density? Explain any three different ways the population density can be measured ,with the help of an example each .
Asnwer the following : (a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range. (b) Thin ozone layer on top of stratosphere is crucial for human survival. Why ? (c) Why is the amount of the momentum transferred by the em waves incident on the surface so small?
(i) Arrange the following compounds in an increasing order of basic strength : `C_(6)H_(5)NH_(2), C_(6)H_(5)N(CN_(3))_(2), (C_(2)H_(5))_(2)NH and CH_(3)NH_(2)` (ii) Arrange the following compounds in a decreasing order of `pK_(b)` values: `C_(2)H_(5)NH_(2), C_(6)H_(5)NHCH_(3), (C_(2)H_(5))_(2) NH and C_(6)H_(5)NH_(2)`
Rerrange the following in an increasing order of their basic strengths: `C_(6)H_(5)NH_(2),C_(6)H_(5)N(CH_(3))_(2),(C_(6)H_(5))_(2)` NH and `CH_(3)NH_(2)`.
(b) Estimate the minimum potential difference needed to reduce `AI_(2)O_(3)` at `500^(@)C` The gibbs energy change for the decomposition reaction `2/3AI_(2)O_(3)rarr4/3AI+O_(2)`is 960 kJ (F=96500 C `mol^(-1))`

Find the value of `lambda` , if four points with position vectors `3 hati + 6 hatj + 9 hatk, hati + 2 hatj + 3 hatk, 2 hati + 3 hatj + hatk and 4 hati + 6 hatj + lambdahat k` are coplanar.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment