Question

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The direction cosines of the vector  are?

  1. -2, 1, -5
  5. -4, -1, -5

Answer (Detailed Solution Below)

Option 4 :

Detailed Solution

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Concept:

The direction cosines of the vector is the corresponding coordinate of the vector divided by the length/Magnitude of the vector. 

 

Calculation:

Here, 

The direction cosines of the given vector = 

Hence, option (4) is correct.

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Exams Tests Super Practice

More Magnitude and Directions of a Vector Questions

Q1.The vector in the direction of the vector î − 2ĵ + 2k̂ that has magnitude 9 is
Q2.The magnitude of the vector 6î + 2ĵ + 3k̂ is
Q3.What are the values of x for which the angle between the vectors 2x2\(\hat{\text{i}}\) + 3x\(\hat{\text{j}}\) + \(\hat{\text{k}}\) and \(\hat{\text{i}}\) −2\(\hat{\text{j}}\) + x2\(\hat{\text{k}}\) is obtuse ?
Q4.Let \(\vec{\text{a}}\), \(\vec{\text{b}}\) and \(\vec{\text{c}}\) be unit vectors lying on the same plane. What is \(\{(3\vec{\text{a}} + 2\vec{\text{b}}) × (5\vec{\text{a}} − 4\vec{\text{c}})\}⋅(\vec{\text{b}} + 2\vec{\text{c}})\) equal to ?
Q5.If l1, m1, n1 and l2, m2, n2 are the direction cosines of two concurrent lines, then the direction cosines of the lines bisecting the angles between them are proportional to :
Q6.Determine the value of p for which  \(p(\hat{i}+\hat{j}+\hat{k})\) is a unit vector?
Q7.Find the value of the given magnitude of the vector, \(\vec{a}=\frac{1}{{\sqrt 3}}\hat i + \frac{1}{{\sqrt 3}}\hat j + \frac{1}{{\sqrt 3}}\hat{k}\) ?
Q8.Determine \(\left| {\overrightarrow a } \right| \rm and\left| {\overrightarrow b } \right|,if(\overrightarrow a + \overrightarrow b ).(\overrightarrow a - \overrightarrow b ) = 8\ and\left| {\overrightarrow a } \right| = 8\left| {\overrightarrow b } \right|\)?
Q9.If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to ?
Q10.What are the direction ratios of the normal to the plane ?

More Vector Algebra Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 
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Q4.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
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Q6.A vector \(\rm \vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in {R}) \) lies in the plane of the vectors, \(\rm \vec{b}=\hat{i}+\hat{j}\) and \(\rm \vec{c}=\hat{i}-\hat{j}+4 \hat{k}\). If \(\rm \vec{a}\) bisects the angle between \(\rm \vec{b}\) and \(\rm \vec{c}\), then
Q7.The vector equation of the plane passing through the intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(\hat{i}-2 \hat{j})=-2\) and the point (1, 0, 2) is:
Q8.Let ABC be a triangle such that \(\overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\vec{b}, \overrightarrow{A B}=\vec{c},|\vec{a}|=6 \sqrt{2},|\vec{b}|=2 \sqrt{3}\) and \(\vec{b} \cdot \vec{c}=12\) Consider the statements : \(\text { (S1): }|(\vec{a} \times \vec{b})+(\vec{c} \times \vec{b})|-|\vec{c}|=6(2 \sqrt{2}-1)\) \(\text { (S2): } \angle A C B=\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then
Q9.Let a unit vector which makes an angle of 60° with 2î + 2ĵ - k̂ and an angle of 45° with î - k̂ be \(\vec{C}\). Then \(\vec{C}+ \left(-\frac{1}{2}\hat{i} + \frac{1}{3\sqrt{2}}\hat{j} - \frac{\sqrt{2}}{3}\hat{k}\right)\) is:
Q10.If a̅, b̅, c̅, d̅ are the position vectors of the points A, B, C, D, respectively, such that no three of them are collinear and a̅ + c̅ = b̅ + d̅. then the quadrilateral ABCD is: 

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
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Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
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