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If the vectors bar(a)=bar(i)+bar(j)+bar(...

If the vectors `bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), and bar(c)=bar(i)+alphabar(j)+betabar(k)` are linearly dependent and `abs(bar(c))=sqrt(3)` then show that `alpha=pm1, beta=1`

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If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), bar(c)=bar(i)+alphabar(j)+betabar(k) are linearly dependent vectors and abs(bar(c))=sqrt(3) then

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Show that bar(a)=bar(i)+2bar(j)+bar(k), bar(b)=2bar(i)+bar(j)+3bar(k) and bar(c)=bar(i)+bar(k) are linearly independent.

Prove that vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) -bar(3j)-5bar(k) and bar(c ) = 3bar(i) - 4bar(j) -4bar(k) are coplanar.

If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9bar(j)" then "bar(c)=

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If bar(a) = bar(i) + 2bar(j)-3bar(k), bar(b) = 3bar(i)-bar(j)+2bar(k) then S.T bar(a)+bar(b), bar(a)-bar(b) are perpendicular.

If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)| .

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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - 1.1 SHORT ANSWER QUESTIONS
  1. ABCDE is a pentagon. If the sum of the vectors bar(AB),bar(AE), bar(...

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  2. If ABCDEF is a regular hexagon with centre O , then P.T bar(AB)+bar(A...

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  3. If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the ...

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  4. Show that the points whose P,V are -2bar(a)+3bar(b)+5bar(c ), bar(a)+2...

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  5. i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vect...

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  6. i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...

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  7. Prove that the following four points are coplanar. i) 4bar(i)+5bar(j...

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  8. If the points whose position vectors are 3bar(i) -2bar(j)-bar(k), 2bar...

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  9. Show that the following vectors are linearly dependent i) bar(i)+bar...

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  10. Show that the following vectors are linearly dependent bar(i)+bar(j)...

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  11. Show that the following vectors are linearly dependent bar(a)-2bar(b...

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  12. Show that the following vectors are linearly dependent bar(a)-2bar(b...

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  13. Show that the following vectors are linearly dependent 3bar(a)-2bar(...

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  14. If the vectors bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4ba...

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  15. If bar(a), bar(b), bar(c) are linearly independent vectors, then show ...

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  16. Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar...

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