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[" 14.The position vectors of the points...

[" 14.The position vectors of the points "A,B,C" are "2hat i+hat j-hat k,3hat i-2hat j+hat k" and "hat i+4_(j-3)}],[" respectively.These points "],[[" (a) form an isosceles triangle "," (b) form a right triangle "],[" (c) are collinear "," (d) form a scalene triangle "]]

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The position vectors of the points A,B,C are 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-hat k respectively.These pooints Form an isosceles triangle Form a right triangle Are collinear Form a scalene triangle

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 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 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.

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 A, B, C are 2hat(i)+hat(j)-hat(k), 3hat(i)-2hat(j)+hat(k) and hat(i)+4hat(j)-3hat(k) respectively. Show that A, B and C are collinear.

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.

Show that the points A(-2hat i+3hat j+5hat k),B(hat i+2hat j+3hat k) and C(7hat i-hat k) are collinear.