AIEEE 2005 | Vector Algebra Question 209 | Mathematics

Let $$a, b$$ and $$c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is :

the Geometric Mean of $$a$$ and $$b$$

the Arithmetic Mean of $$a$$ and $$b$$

equal to zero

the Harmonic Mean of $$a$$ and $$b$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ are non coplanar vectors and $$\lambda $$ is a real number then

$$\left[ {\lambda \left( {\overrightarrow a + \overrightarrow b } \right)\,\,\,\,\,\,\,\,{\lambda ^2}\overrightarrow b \,\,\,\,\,\,\,\,\lambda \overrightarrow c } \right] = \left[ {\overrightarrow a \,\,\,\,\,\,\,\,\overrightarrow b + \overrightarrow c \,\,\,\,\,\,\,\,\overrightarrow b } \right]$$ for :

exactly one value of $$\lambda $$

no value of $$\lambda $$

exactly three values of $$\lambda $$

exactly two values of $$\lambda $$

AIEEE 2005

MCQ (Single Correct Answer)

-1

For any vector $${\overrightarrow a }$$ , the value of $${\left( {\overrightarrow a \times \widehat i} \right)^2} + {\left( {\overrightarrow a \times \widehat j} \right)^2} + {\left( {\overrightarrow a \times \widehat k} \right)^2}$$ is equal to :

$$3{\overrightarrow a ^2}$$

$${\overrightarrow a ^2}$$

$$2{\overrightarrow a ^2}$$

$$4{\overrightarrow a ^2}$$

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