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Find the magnitude of a given by veca=(h...

Find the magnitude of a given by `veca=(hati+3hatj+hatk)xx(-hati+3hatk)`

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To find the magnitude of the vector \(\vec{a} = (\hat{i} + 3\hat{j} + \hat{k}) \times (-\hat{i} + 3\hat{k})\), we will follow these steps: ### Step 1: Set up the cross product We need to calculate the cross product of the two vectors: \[ \vec{a} = \hat{i} + 3\hat{j} + \hat{k} \] and ...
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(i) Find the sum of vectors veca=hati-2hatj+hatk , vecb=-2hati+4hatj+5hatk , and vecc=hati-hatj-7hatk (ii) Find the magnitude of the vector veca=3hati-2hatj+6hatk .

Prove that: (2hati+3hatj)xx(hati+2hatj)=hatk

Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the direction perpendicular to the direction of vector veca = hati + hatj +hatk is hati - hatj Statement 2: A component of vector in the direction of veca = hati + hatj + hatk is 2hati + 2hatj + 2hatk

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr= 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk) .

Find the scalar and vector products of two vectors veca=(2hati-3hatj+4hatk) and vecb(hati-2hatj+3hatk) .

Find a unit vector perpendicular to the plane of two vectros. veca=hati-hatj+2hatk and vecb=2hati+3hatj-hatk

Find magnitude of A-2 B +3 C, where, A = 2hati+3hatj, B = hati + hatj and c =hatk.

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors " "veca=2hati+3hatj-hatk and vecb=hati-2hatj+hatk .

Find the unit vector perpendicular to the vectors vecA=(hati+2hatj-3hatk)andvecB=(-hati+hatj-hatk)

Find the scalar product of vectors veca=2hati-hatj+2hatk and vecb=hati-3hatj-5hatk

AAKASH INSTITUTE ENGLISH-VECTOR ALGEBRA-TRY YOURSELF
  1. Classify the following as scalars and vectors : Time Distance Di...

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  2. Represent the following graphically : A displacement of 70 km, 60^(@...

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  3. In the given figure, vectors which are Collinear Equal Collinear...

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  4. In the given figure, identify the following vectors : Coinitial ...

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  5. Vectors drawn the origin O to the points A , B and C are respectively ...

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  6. If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R ...

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  7. If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prove that vec A B= vec C Ddot

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  8. If the position vector veca of a point (m,5) is such that |veca|=13, f...

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  9. (i) Find the sum of vectors veca=hati-2hatj+hatk , vecb=-2hati+4hat...

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  10. (i) Find the unit vector in the direction of veca+vecb if veca=2hati-h...

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  11. Find the distance between points A(2,5,7), B(1,3,5), by using vector ...

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  12. Show that the points A (-2,3,5), B (1,2,3) and C (7,0,-1) are collinea...

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  13. Find the mid point of the line segment joining the points P(2hati+3hat...

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  14. Find the position vector of a point R which divides the line joining ...

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  15. Find the angle between the vectors veca and vecb if |veca|=2|vecb|=3...

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  16. Find the projection of vector veca=5hati-hatj-3hatk on the vector vecb...

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  17. Show that the points with position vectors vec a-2 vec b+3 vec c ,\ -...

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  18. Let veca and vecb be two vectors of the same magnitude such that the a...

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  19. Find the magnitude of a given by veca=(hati+3hatj+hatk)xx(-hati+3hatk)

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  20. Find the area of the triangle whose vertices are A(3,-1,2),\ B(1,-1,-3...

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