The value of p such that the vectors hat...

The value of p such that the vectors `hat(i) + 3hat(j) - 2hat(k), 2hat(i) - hat(j) + 4hat(k)` and `3hat(i) + 2hat(j) + p hat(k)` are coplanar is

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Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

The unit vector perpendicular to the vectors hat(i) -hat(j) + hat(k), 2hat(i) + 3hat(j) -hat(k) is

For what value of 'a' the vectors 2hat(i) - 3hat(j) + 4hat(k) and ahat(i) + 6hat(j) - 8hat(k) are collinear ?

Show that the vectors vec(a)=hat(i)-2hat(j)+3hat(k) vec(b)=-2i+3hat(j)-4hat(k)vec( c) =hat(i) -3 hat(j) +5hat(k) are coplanar.

Find the vector equation of the plane passing through three points with position vectors (hat(i) + hat(j) - 2 hat(k)),(2 hat(i) - hat(j) + hat(k)) and (hat(i) + 2 hat(j) + hat(k)) . Also find the coordinates of the point of intersection of this plane and the line vec(r) = (3 hat(i) - hat(j) - hat(k)) + lambda (2 hat(i) - 2 hat(j) + hat(k)) .

Show that the four points A, B, C and D with position vectors 4hat(i) + 5hat(j) + hat(k) - hat(j) - hat(k), 3hat(i) + 9hat(j) + 4hat(k) and 4(-hat(i) + hat(j) + hat(k)) respectively are coplanar.

If the vectors 2hat(i) + 3hat(j) - 6hat(k) and 4hat(i) - m hat(j) - 12 hat(k) are parallel find m.

Find the sum of vectos a = hat(i)- 2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k) and c=hat(i)-6hat(j)-7hat(k) .

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

KCET PREVIOUS YEAR PAPERS-MODEL TEST PAPER 9-Mathematics

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