The position vectors of point A ,B ,a...

The position vectors of point `A ,B ,a n dC` are ` hat i+ hat j+ hat k , hat i+5 hat j- hat ka n d2 hat i+3 hat j+5 hat k ,` respectively. Then greatest angel of triangle `A B C` is `120^0` b. `90^0` c. `cos^(-1)(3//4)` d. none of these

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Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(k), 2hat(i)-hat(j)+hat(k) " and " hat(i)-3hat(j)-5hat(k) respectively. Show that ABC is right-angled triangle.

The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) " and " 3hat(i)+6hat(j)-3hat(k) respectively. Show that the points form a right-angled triangle.

if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , Find vec a . vec b =?

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot Then find [vec a vec b vec c]

The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(k), hat(i)+2hat(j)+4hat(k) " and " 3hat(i)+10hat(j)-6hat(k) respectively. Show that the points A, B and C are collinear.

If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2hat(k), 2hat(i)+3hat(j)+3hat(k) " and " -hat(i)-2hat(j)+3hat(k) respectively, show that ABC is an isosceles triangle.

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , hat i+2 hat j+3 hat ka n d3 hat i+ hat j+2 hat k respectively. Find the shortest distance between point B and plane O A Cdot

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

Let vec a , vec ba n d vec c be three non-coplanar vectors and v...
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vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors an...
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The position vectors of point A ,B ,a n dC are hat i+ hat j+ hat k...
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Let vec a(x)=(sin x) hat i+(cosx) hat j a n d vec b(x)=(cos2x) hat i+...
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If vec a=2 hat i+ hat j+ hat k , vec b= hat i+2 hat j+2 hat k , vec c=...
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If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...
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If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...
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The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...
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Let vec a=- hat i- hat k , vec b=- hat i+ hat ja n d vec c= hat i+2 h...
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Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. L...
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If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...
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Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i...
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Find the work done by the force F=3 hat i- hat j-2 hat k acrting on ...
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Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, ve...
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find the angle between the vectors vec a= hat i+ hat j - hat k and ve...
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O A B C is regular tetrahedron in which D is the circumcentre of O...
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In the quadrilateral ABCD, the diagonals AC and BD are equal and perpe...
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If vece(1),vece(2),vece(3)and vecE(1),vecE(2),vecE(3) are two sets of ...
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Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=...
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Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...
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