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The sides of a parallelogram are 2hat(i)...

The sides of a parallelogram are `2hat(i)+4hat(j)-5hat(k) " and " hat(i)+2hat(j)+3hat(k)`. Then the unit vector parallel to one of the diagonals is -

A

`1/7(3hat(i)+6hat(j)-2hat(k))`

B

`1/7(3hat(i)-6j-2hat(k))`

C

`1/sqrt(69)(-hat(i)-2hat(j)+8hat(k))`

D

`1/sqrt(69)(hat(i)+2hat(j)+8hat(k))`

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A, C
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The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 hat j+3 hat k . The unit vector parallel to one of the diagonals is a. 1/7(3 hat i+6 hat j-2 hat k) b. 1/7(3 hat i-6 hat j-2 hat k) c. 1/(sqrt(69))( hat i+6 hat j+8 hat k) d. 1/(sqrt(69))(- hat i-2 hat j+8 hat k)

If vec(AB)=2hat(i)-4hat(j)+5hat(k) " and " vec(BC)=hat(i)-2hat(j)-3hat(k) in parallelogram ABCD, find a unit vector in direction parallel to the diagonal vec(AC) of the parallelogram.

If vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k) , find a unit vector in a direction parallel to vector (vec(a)-vec(b)) .

Find a unit vector in direction parallel to the sum of the vectors vec(a)=2hat(i)+4hat(j)-5hat(k) " and " vec(b)=hat(i)+2hat(j)+3hat(k) , find also the direction cosines of this vector.

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

(i) Determine the value of p for which the vectors phat(i)-5hat(j) " and " 2hat(i)-3hat(j) are collinear. (ii) The sides AB and BC of the triangle ABC are represented by the vectors 2hat(i)-hat(j)+2hat(k) " and " hat(i)+3hat(j)+5hat(k) respectively, find the vector representing side CA of the triangle ABC.

If vectors vec(alpha)=2hat(i)+3hat(j)-6hat(k) " and " vec(beta)=phat(i)-hat(j)+2hat(k) are parallel, then the value of p is -

If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " vec(c)=hat(i)-2hat(j)+hat(k) find a unit vector in a direction parallel to vector (2vec(a)-vec(b)+3vec(c)) .

The scaler product of the vector hat (i) + hat (j) + hat (k) with the unit vector along the sum of vectors 2 hat (i) + 4 hat (j) - 5 hat (k) and lambda hat (i) + 2 hat (j) + 3 hat (k) is equal to one . Find the value of lambda

If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

CHHAYA PUBLICATION-VECTOR-SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION
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  13. ABCD is a parallelogram. L is a point on BC which divides BC in the ra...

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  14. Consider the regular hexagon ABCDEF with centre at O (origin). vec(A...

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  15. Consider the regular hexagon ABCDEF with centre at O (origin). Five ...

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  16. Consider the regular hexagon ABCDEF with centre at O (origin). vec(A...

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